Analytic Geometry 1

8/19/2019 Analytic Geometry 1

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Analytic Geometry 1Problem 1: ECE Board April 1999

The linear distance between –4 and 17 on the number line is

•

A. 13• B. 21

• C. –17

• D. –13Problem 2: EE Board April 1994

Find the distance between A (4 –3! and B (–2 "!.

• A. 11

•

B. #• C. 1$

• D.%Problem 3:

&' the distance between oints (3 )! and (% 7! is 13 then ) is e*ual to

• A. " or –"

• B. " or 1#

•

C. 1#• D. –" or 1#

Problem 4:

Find the coordinate o' a oint e*uidistant 'rom (1 +,! (" +,! and (, +1!.

• A. (2 +2!

• B. (3 +2!

• C. (3 +3!

•D. (2 +3!

Problem 5: EE Board April 1995

The line se-ment connectin- ( ,! and (# )! is bisected b) the oint (7 3!.Find the /alues o' and ).

• A. 14 ,

• B. 33 12


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• C. " $

• D. 14 ,Problem 6:

&' (+2 +4! is the midoint o' (, +7! and ( )! then the /alues o' and ) are• A. 0 2 ) 0 1

• B. 0 +1$ ) 0 +1

• C. 0 1$ ) 0 +1

• D. 0 +% ) 0 +1Problem 7: ECE Board Noember 199!

Determine the coordinates o' the oint which is three+'ths o' the wa) 'romthe oint (2 +"! to the oint (+3 "!.

• A. (+1 1!

• B. (+2 +1!

• C. (+1 +2!

• D. (1 +1!Problem !: ECE Board April 199!

The se-ment 'rom (+1 4! to (2 +2! is etended three times its own len-th. The terminal oint is

• A. (11 +24!

• B. (+11 +2$!

• C. (11 +1%!

• D. (11 +2$!Problem 9:

The oints (a 1! (b 2! and (c 3! are collinear. hich o' the 'ollowin- is true

• A. c – b 0 c – a

• B. c – b 0 b – a

• C. c – a 0 a – b

• D. c – a 0 b – aProblem 1":


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&' the sloe o' the line connectin- the ori-in and oint is 5 nd theabscissa o' i' its ordinate is ,.

• A. 2

• B. ,

• C. 7

• D. %Problem 11: ECE Board April 1999

Find the inclination o' the line assin- throu-h (+" 3! and (1$ 7!.

• A. 14.73

• B. 14.#3

• C. 14.%3

• D. 14.,3Problem 12:

Find the an-le 'ormed b) the lines 2 6 ) – % 0 $ and 6 3) 6 4 0 $.

• A. 3$

• B. 3"

• C. 4"

• D. ,$

Problem 13:

Find the an-le between the lines 3 6 2) 0 , and 6 ) 0 ,.

• A. 12 2$8

• B. 11 1#8

• C. 14 2"8

• D. 13 $,8Problem 14:

hat is the acute an-le between the lines ) 0 3 6 2 and ) 0 4 6 #

• A. 4.4

• B. 2%.3

• C. ".2

• D. 1%.,


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Problem 15: EE Board #ctober 1997

Find the distance o' the line 3 6 4) 0 " 'rom the ori-in.

• A. 4

• B. 3

• C. 2

• D. 1Problem 16: CE Board Noember 1992

The two oints on the lines 2 0 3) 6 4 0 $ which are at a distance 2 'romthe line 3 6 4) – , 0 $ are

• A. (+" 1! and (+" 2!

•

B. (,4 +44! and (4 +4!• C. (% %! and (12 12!

• D. (44 +,4! and (+4 4!Problem 17: CE Board Noember 1992

The distance 'rom the oint (2 1! to the line 4 – 3) 6 " 0 $ is

• A. 1

• B. 2

•

C. 3• D. 4

Problem 1!: CE Board Noember 1996

Determine the distance 'rom (" 1$! to the line – ) 0 $.

• A. 3.33

• B. 3."4

• C. 4.23

•

D. ".4"Problem 19:

The distance 'rom a oint (1 3! to the line 4 6 3) 6 12 0 $ is

• A. 4 units

• B. " units


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• C. , units

• D. 7 unitsProblem 2": CE Board $ay 1992

Find the distance between the -i/en lines 4 – 3) 0 12 and 4 – 3) 0 +%.• A. 3

• B. 4

• C. "

• D. ,Problem 21: EE Board April 1995

Find the distance between the lines 3 6 ) – 12 0 $ and 3 6 ) – 4 0 $.

Problem 22: $E Board #ctober 1996

hat is the len-th o' the line with a sloe o' 493 'rom a oint (, 4! to the )+ais

• A. 1$

• B. 2"

• C. "$

• D. 7"Problem 23: $E Board April 199!

Find the sloe o' the line dened b) ) – 0 ".• A. 1

• B. 194

• C. +192

• D. " 6 Problem 24: CE Board Noember 1995


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hat is the sloe o' the line 3 6 2) 6 1 0 $

• A. 392

• B. 293

• C. +392

• D. +293Problem 25: ECE Board Noember 199"

&n a Cartesian coordinates the /ertices o' a trian-le are dened b) the'ollowin- oints: (+2 $! and (3 3!. hat is the area

• A. % s*. units

• B. # s*. units

• C. 1$ s*. units

• D. 11 s*. unitsProblem 26: EE Board April 1994

;i/en three /ertices o' a trian-le whose coordinates are A (1 1! B (3 +3!and (" +3!. Find the area o' the trian-le.

• A. 3

• B. 4

• C. "

• D. ,Problem 27: ECE Board Noember 199"

&n a Cartesian coordinates the /ertices o' a s*uare are: (1 1! ($ %! (4 "!and (+3 4!. hat is the area

• A. 2$ s*. units

• B. 3$ s*. units

• C. 2" s*. units

•

D. 3" s*. unitsProblem 2!: EE Board April 1997

A line asses thru (1 +3! and (+4 2. rite the e*uation o' the line in sloe+intercet 'orm.

• A. ) – 4 0

• B. ) 0 + – 2


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• C. ) 0 – 4

• D. ) – 2 0 Problem 29: EE Board #ctober 1997

hat is the +intercet o' the line assin- throu-h (1 4! and (4 1!• A. 4."

• B. "

• C. 4

• D. ,Problem 3": $E Board April 1997

Find the e*uation o' the strai-ht line with a sloe o' 3 and a )+intercet o' 1.

•

A. 3 6 ) – 1 0 $• B. 3 – ) 6 1 0 $

• C. 6 3) 6 1 0 $

• D. – 3) – 1 0 $Problem 31: ECE Board April 1999

&' the oints (+2 3! ( )! and (+3 "! lie on a strai-ht line then the e*uationo' the line is


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A line with an inclination o' 4" asses throu-h (+"92 +#92!. hat is the +coordinate o' a oint on the line i' its corresondin- )+coordinate is ,

• A. ,

• B. 7

• C. %

• D. #Problem 34:

Find the e*uation o' the line assin- throu-h the ori-in and with a sloe o' ,

• A. ) – , 0 $

• B. ) 0 +,

• C. 6 ) 0 +,

• D. , 6 ) 0 $Problem 35:

Find the e*uation o' the line i' the +intercet and )+intercet are +2 and 4resecti/el).

• A. ) – 2 – 4 0 $

• B. ) 6 2 – 4 0 $

• C. ) – 2 6 4 0 $

• D. ) 6 2 6 4 0 $Problem 36: ECE Board April 199!

Determine B such that 3 6 2) – 7 0 $ is erendicular to 2 – B) 6 2 0 $.

• A. "

• B. 4

• C. 3

• D. 2

Problem 37: The line 2 – 3) 6 2 0 $ is erendicular to another line =1 o' un>nowne*uation. Find the sloe o' =1.

• A. 392

• B. +392

• C. 293


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• D. +293Problem 3!:

A line throu-h (+" 2! and (1 +4! is erendicular to the line throu-h ( +7!and (% 7!. Find the .

• A. +4

• B. +"

• C. +,

• D. +1#93Problem 39: CE Board $ay 1996

hat is the e*uation o' the line that asses thru (4 $! and is arallel to theline – ) – 2 0 $

• A. – ) 6 4 0 $

• B. 6 ) 6 4 0 $

• C. – ) – 4 0 $

• D. – ) 0 $Problem 4":

Find the e*uation o' the line throu-h oint (3 1! and is erendicular to theline 6 ") 6" 0 o.

•

A. " – 2) 0 14• B. " – ) 0 14

• C. 2 – ") 0 14

• D. 2 6 ") 0 14Problem 41:

Find the e*uation o' the erendicular bisector o' the line ?oinin- (" $! and (+7 3!.

• A. % 6 2) 6 11 0 $

• B. % – 2) 6 11 0 $

• C. % – ) 6 11 0 $

• D. % 6 ) 6 11 0 $Problem 42:


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hich o' the 'ollowin- lines is arallel to the line 3 – 2) 6 , 0 $

• A. 3 6 2) – 12 0 $

• B. 4 – #) 0 ,

• C. 12 6 1%) 0 1"

• D. 1" – 1$) – # 0 $Problem 43:

The e*uation o' the line throu-h (+3 +"! arallel to 7 6 2) – 4 0 $ is

• A. 7 6 2) 6 31 0 $

• B. 7 – 2) 6 3$ 0 $

• C. 7 – 2) – 4 0 $

• D. 2 6 7) 6 3$ 0 $Problem 44:

hat is the e*uation o' the line ?oinin- the oints (3 +2! and (+7 ,!

• A. 2 6 3) 0 $

• B. 4 – ") 0 22

• C. 4 6 ") 0 2

• D. " 6 4) 0 7Problem 45:

hat is the e*uation o' the line assin- throu-h (+2 ,! with the +intercethal' the )+intercet

• A. – ) 0,

• B. 2 6 2) 6 2 0 $

• C. 3 – ) 6 2 0 $

• D. 2 6 ) – 2 0 $Problem 46: CE Board $ay 1997

Find the sloe o' a line ha/in- a arametric e*uation o' 0 2 6 t and ) 0 " –3t.

• A. 2

• B. 3

• C. +2


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• D. +3Problem 47: CE Board $ay 199!

Find the sloe o' the line ha/in- a arametric e*uation ) 0 4t 6 , and 0 t6 1.

• A. 1

• B. 2

• C. 3

• D. 4Problem 4!: ECE Board April 1999

Two /ertices o' a trian-le are (2 4! and (+2 3! and the area is 2 s*uare unitsthe locus o' the third /erte is

• A. 4 – ) 0 14

• B. 4 6 4) 0 14

• C. 6 4) 0 12

• D. – 4) 0 +14Problem 49: ECE Board April 199!

Find the area o' the trian-le which the line 2 – 3) 6 , 0 $ 'orms with thecoordinate ais.

•

A. 3• B. 4

• C. "

• D.2Problem 5": ECE Board Noember 199!

A line asses throu-h oint (2 2!. Find the e*uation o' the line i' the len-tho' the line se-ment interceted b) the coordinate aes is the s*uare root o'".

• A. 2 6 ) – 2 0 $

• B. 2 – ) – 2 0 $

• C. 2 – ) 6 2 0 $

• D. 2 6 ) 6 2 0 $


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"1. @tate the *uadrant in which the coordinate (1" +2! lies.

• A. &

• B. &

• C. &&

• D. &&&

"2. ' what *uadrant is A i' sec A is ositi/e and csc A is ne-ati/e

• A. &&&

• B. &

• C. &

• D. &&

"3. The se-ment 'rom (+1 4! to (2 +2! is etended three times its ownlen-th. The terminal oint is

• A. (11 +1%!

• B. (11 +24!

• C. (11 +2$!

• D. (+11 +2$!"4. The midoint o' the line se-ment between 1( )! and 2(+2 4! is m(2+1!. Find the coordinate o' 1.

• A. (, +"!

• B. (" +,!

• C. (, +,!

• D. (+, ,!

"". Find the coordinates o' the oint (24! with resect to the translated aiswith ori-in at (13!.

• A. (1 +1!

• B. (1 1!

• C. (+1 +1!

• D. (+1 1!

",. Find the median throu-h (+2 +"! o' the trian-le whose /ertices are (+, 2!(2 +2! and (+2 +"!.


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• A. 3

• B. 4

• C. "

• D. ,

"7. Find the centroid o' a trian-le whose /ertices are (2 3! (+4 ,! and (2+,!.

• A. ($ 1!

• B. ($ +1!

• C. (1 $!

• D. (+1 $!

"%. Find the area o' trian-le whose /ertices are A (+3 +1! B(" 3! and (2 +%!

• A. 34

• B. 3,

• C. 3%

• D. 32

"#. Find the distance between the oints (4 +2! and (+" 1!

• A. 4.%#7

• B. %.#47

• C. 7.14#

• D. #.4%7

,$. Find the distance between A(4 +3! and B(+2 "!.

• A. 11

• B. %

• C. #

• D. 1$

,1. &' the distance between the oints (% 7! and (3 )! is 13 what is the/alue o' )

• A. "


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• B. +1#

• C. 1# or +"

• D. " or +1#

,2. The distance between the oints (sin cos ! and (cos +sin ! is:

• A. 1

• B. 2

• C. 2 sin cos

• D. 4 sin cos

,3. Find the distance 'rom the oint (2 3! to the line 3 6 4) 6 # 0 $.

• A. "

• B. ".4

• C. ".%

• D. ,.2

,4. Find the distance 'rom the oint (" +3! to the line 7 + 4) + 2% 0 $.

• A. 2.,2

• B. 2.3,

• C. 2.4%• D. 2."4

,". ow 'ar is the line 3 – 4) 6 1" 0 $ 'rom the ori-in

• A. 1

• B. 2

• C. 3

• D. 4

,,. Determine the distance 'rom (" 1$! to the line – ) 0 $

• A. 3.%,

• B. 3."4

• C. 3.,%


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• D. 3.72

,7. The two oints on the lines 2 6 3) 64 0 $ which are at distance 2 'romthe line 3 6 4) – , 0 $ are:

•

A. (+% +%! and (+1, +1,!• B. (+44 ,4! and (+" 2!

• C. (+"." 1! and (+" 2!

• D. (,4 +44! and (4 +4!

,%. The intercet 'orm 'or al-ebraic strai-ht+line e*uation is:

• A. (a9! 6 ()9b! 0 1

• B. ) 0 m 6 b

• C. A 6 B) 6 C 0 $

• D. (9a! 6 ()9b! 0 1

,#. Find the sloe o' the line dened b) ) – 0 "

• A. 1

• B. +192

• C. E

• D. " 6

7$. The sloe o' the line 3 6 2) 6 " 0 $ is:

• A. +293

• B. +392

• C. 392

• D. 293

71. Find the sloe o' the line whose arametric e*uation is ) 0 " – 3t and 02 6 t.

• A. 3

• B. +3

• C. 2

• D. +2


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72. Find the sloe o' the cur/e whose arametric e*uations are

0 +1 6 t

) 0 2t

• A. 2

• B. 3

• C. 1

• D. 4

73. Find the an-le that the line 2) – # – 1% 0 $ ma>es with the +ais.

• A. 74.77

• B. 4."• C. 47.77

• D. 77.47

74. hich o' the 'ollowin- is erendicular to the line 93 6 )94 0 1

• A. – 4) – % 0 $

• B. 4 – 3) – , 0 $

• C. 3 – 4) – " 0 $

• D. 4 6 3) – 11 0 $

7". Find the e*uation o' the bisector o' the obtuse an-le between the lines2 6 ) 0 4 and 4 + 2) 0 7

• A. 4) 0 1

• B. % 0 1"

• C. 2) 0 3

• D. % 6 4) 0 ,

7,. The e*uation o' the line throu-h (1 2! and arallel to the line 3 – 2) 6 40 $ is:

• A. 3 – 2) 6 1 0 $

• B. 3 – 2) – 1 0 $

• C. 3 6 2) 6 1 0 $


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• D. 3 6 2) – 1 0 $

77. &' the oints (+3 +"! ( )! and (3 4! lie on a strai-ht line which o' the'ollowin- is correct

•

A. 3 6 2) – 1 0 $• B. 2 6 3) 6 1 0 $

• C. 2 6 3) – 1 0 $

• D. 3 – 2) – 1 0 $

7%. ne line asses throu-h the oints (1 #! and (2 ,! another line assesthrou-h (3 3! and (+1 "!. The acute an-le between the two lines is:

• A. 3$

•

B. 4"• C. ,$

• D. 13"

7#. The two strai-ht lines 4 – ) 6 3 0 $ and % – 2) 6 , 0 $

• A. &ntersects at the ori-in

• B. Are coincident

• C. Are arallel

• D. Are erendicular

%$. A line which asses throu-h (" ,! and (+3. +4! has an e*uation o'

• A. " 6 4) 6 1 0 $

• B. " + 4) + 1 0 $

• C. " + 4) 6 1 0 $

• D. " 6 ) + 1 0 $

%1. Find the e*uation o' the line with sloe o' 2 and )+intercet o' +3.

• A. ) 0 +3 6 2

• B. ) 0 2 – 3

• C. ) 0 293 6 1

• D. ) 0 3 – 2


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%2. hat is the e*uation o' the line that asses throu-h (4 $! and is arallelto the line – ) – 2 0 $

• A. ) 6 6 4 0 $

• B. ) + 6 4 0 $

• C. ) + + 4 0 $

• D. ) 6 + 4 0 $

%3. Determine B such that 3 6 2) – 7 0 $ is erendicular to 2 – B) 6 2 0$

• A. 2

• B. 3

• C. 4

• D. "

%4. The e*uation o' a line that intercets the +ais at 0 4 and the )+ais at) 0 +, is:

• A. 2 – 3) 0 12

• B. 3 6 2) 0 12

• C. 3 – 2) 0 12

• D. 2 – 37 0 12

%". ow 'ar 'rom the )+ais is the center o' the cur/e 22 6 2)2 6 1$ – ,) –"" 0 $

• A. +3.$

• B. 2.7"

• C. +3.2"

• D. 2."

%,. Find the area o' the circle whose center is at (2+"! and tan-ent to the

line 4 6 3) – % 0 $.• A. ,G

• B. #G

• C. 3G

• D. 12G%7. Determine the area enclosed b) the cur/e 2 – 1$ 6 4) 6 )2 0 1#,


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• C. 7

• D. ,#3. The diameter o' a circle described b) #2 6 #)2 0 1, is:

• A. 1,9#

• B. 493

• C. 4

• D. %93#4. Find the center o' the circle 2 6 )2 – , 6 4) – 23 0 $.

• A. (3 +2!

• B. (3 2!

• C. (+3 2!

•

D. (+3 +2!#". Determine the e*uation o' the circle whose center is at (4 "! andtan-ent to the circle whose e*uation is 2 6 )2 6 4 6 ,) – 23 0 $.

• A. 2 6 )2 – % 6 1$) – 2" 0 $• B. 2 6 )2 6 % – 1$) 6 2" 0 $

• C. 2 6 )2 – % – 1$) 6 2" 0 $• D. 2 6 )2 – % – 1$) – 2" 0 $

#,. The e*uation o' the circle with center at (+2 3! and which is tan-ent tothe line 2$ – 21) – 42 0 $.

•

A. 2

6 )2

6 4 – ,) – 12 0 $• B. 2 6 )2 6 4 – ,) 6 12 0 $

• C. 2 6 )2 6 4 6 ,) – 12 0 $• D. 2 6 )2 – 4 – ,) – 12 0 $

#7. A circle has a diameter whose ends are at (+3 2! and (12 +,!. &tsH*uation is:

• A. 42 6 4)2 – 3, 6 1,) 6 1#2 0 $• B. 42 6 4)2 – 3, 6 1,) – 1#2 0 $• C. 42 6 4)2 – 3, – 1,) – 1#2 0 $

• D. 42 6 4)2 – 3, – 1,) 6 1#2 0 $

#%. Find the e*uation o' the circle with center on 6 ) 0 4 and " 6 2) 6 10 $ and ha/in- a radius o' 3.

• A. 2 6 )2 6 , – 1,) 6 ,4 0 $• B. 2 6 )2 6 % – 14) 6 2" 0 $

• C. 2 6 )2 6 , – 14) 6 4# 0 $


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• D. 2 6 )2 6 , – 14) 6 3, 0 $

##. &' (3 +2! lies on the circle with center (+1 1! then the e*uation o' thecircle is:

• A. 2 6 )2 6 2 – 2) – 23 0 $

• B. 2 6 )2 6 4 – 2) – 21 0 $• C. 2 6 )2 6 2 – ) – 33 0 $• D. 2 6 )2 6 4 – 2) – 27 0 $

1$$. Find the e*uation o' > 'or which the e*uation 2 6 )2 6 4 – 2) – > 0 $reresents a oint circle.

• A. "

• B. +"

• C. ,

•D. +,

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Analytic Geometry 1