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Math Worksheets Name: __________
Date: ___________
β¦ So Much More Online! Please visit: www.EffortlessMath.com
Classifying a Conic Section (in Standard Form)
Classify each conic section and write its equation in standard form.
1) π₯2 β 4π¦2 + 6π₯ β 8π¦ + 1 = 0
2) 3π₯2 + 3π₯ + π¦ + 79 = 0
3) π₯2 + π¦2 + 4π₯ β 2π¦ β 18 = 0
4) β π¦2 + π₯ + 8π¦ β 17 = 0
5) 49π₯2 + 9π¦2 + 392π₯ + 343 = 0
6) β 9π₯2 + π¦2 β 72π₯ β 153 = 0
7) β 2π¦2 + π₯ β 20π¦ β 49 = 0
8) βπ₯2 + 10π₯ + π¦ β 21 = 0
Classify each conic section. (Not in Standard Form)
9) π₯2 + π¦2 β 8π₯ + 8π¦ β 4 = 0
10) π¦ = 6π₯2 β 60π₯ + 149
11) π₯2 β 4π₯ + 4π¦2 β 32π¦ + 32 = 0
12) π₯2β 2π₯ β 36π¦2 β 360π¦ β 935 = 0
13) π¦ = 6π₯2 β 60π₯ + 149
14) π₯2 + π¦2β 8π₯ + 8π¦ β 4 = 0
15) π₯2 + π¦2 + 6π₯ + 10π¦ + 33 = 0
16) π₯2β 4π₯ β 36π¦2 + 288π¦ β 608 =
0
17) 9π₯2 + 4π¦2 + 16π¦ β 128 = 0
18) π₯2 + 8π₯ β 25π¦2 + 50π¦ β 34 = 0
19) π¦ = 6π₯2 + 60π₯ + 155
20) 4π₯2 + 9π¦2 β 54π¦ + 45 = 0
21) β 9π₯2 β 54π₯ + 4π¦2β 40π¦ β 125 = 0
22) π₯2β 4π₯ + 4π¦2 β 32π¦ + 32 = 0
Math Worksheets Name: __________
Date: ___________
β¦ So Much More Online! Please visit: www.EffortlessMath.com
Answers
Classifying a Conic Section
1) Hyperbola, (π₯ + 3)2
4 β (π¦ + 1)2 = 1
2) Parabola, π¦ = β3(x + 5)2 β 4 3) Circle, (π₯ + 2)2 + (π¦ β 1)2 = 23 4) Parabola, x = (π¦ β 4)2 + 1
5) Ellipse, (π₯+4)2
9 +
π¦2
49 = 1
6) Hyperbola, π¦2
9 β (π₯ + 4)2 = 1
7) Parabola, π₯ = 2(π¦ + 5)2 β 1 8) Parabola, π¦ = (π₯ β 5)2 β 4 9) Circle
10) Parabola
11) Ellipse
12) Hyperbola
13) Parabola
14) Circle
15) Circle
16) Hyperbola
17) Ellipse
18) Hyperbola
19) Parabola
20) Ellipse
21) Hyperbola
22) Ellipse