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1 Revision Exercise 8

Solutions to Revision Exercise 8 (Ho Soo Thong & Khor Nyak Hiongs Panpac Additional Mathematics)

Solved by: Dr Lee Chu Keong (ascklee@gmail.com)

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2 Revision Exercise 8

Revision Exercise 8 This PDF file only contains solutions. For the questions, please refer to Ho Soo Thong

and Khor Nyak Hiongs textbook, Additional Mathematics.

Question 1

:

Substitute into :

(

)

Substitute into :

Foot of the perpendicular:

Distance from to :

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3 Revision Exercise 8

( )

Foot of the perpendicular is the midpoint between and :

(

)

Point is

Question 2(a)

(

)

(

)

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4 Revision Exercise 8

Question 2(b)

Point of intersection D is (

)

Question 2(c)

(

)

Question 2(d)

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5 Revision Exercise 8

Question 3

1 2 3 4 5

6.57 10.79 17.75 29.16 47.92

1.88 2.38 2.88 3.37 3.87

Rearranging,

(

)

Question 4

Dividing throughout by :

(

)

So, equation of line:

(

)

When

,

(

)

(

)

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6 Revision Exercise 8

Question 5(a)

In Point Q, the y-coordinate is 0:

Rearranging :

Substituting into :

Substituting into :

Question 5(b)

(

)

Question 5(c)

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7 Revision Exercise 8

When :

Therefore, the perpendicular bisector passes through .

Question 6(a)

Start with the general equation for circles:

There are three unknowns: , , and .

To solve the three unknowns, three equations are needed.

They will be constructed from the three points that the circle passes through: ,

, and .

Point 1 (ORIGIN):

Point 2:

Point 3:

Substitute (1) into (2) and (3), and magically, they will be simplified:

4(4) gives:

(6)(5):

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8 Revision Exercise 8

Substitute into (4):

Lastly, we calculate :

Finally, the equation of the circle:

Question 6(b)

Comparing coefficients:

Therefore, the centre of the circle is .

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9 Revision Exercise 8

The y-coordinate is the same as the x-coordinate.

(

)

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