CLASSIFYING CONIC SECTIONS BY ITS GENERAL EQUATION WORKSHEET
Put each of the following equations in standard form and classify the conic.
Problem 1 :
9y2 – x2 + 2x + 54y + 62 = 0
Problem 2 :
4x2 + y2 - 8x + 4y - 16 = 0
Problem 3 :
x2 + y2 + 6x - 4y + 12 = 0
Problem 4 :
x2 - 2y + 16x + 28 = 0
Answer Key
1)
(x - 1)2/144 - (y + 3)2 / 16 = 1
It is in the form of (x - h)2/a2 - (y - k)2 / b2 = 1
It is a hyperbola.
2)
(x - 1)2/4 + (y + 2)2/16 = 1
It is in the form of (x - h)2/a2 + (y - k)2 / b2 = 1
It is a ellipse
3)
(x + 3)2 + (y - 2)2 = 1
It is in the form of (x - h)2 + (y - k)2 = r2
It is a circle.
4)
y = (1/2) (x + 4)2 + 6
It is in the form, y = 4a (x - h)2 + k
So, it is parabola.
Classify each conic section and write its equation in standard form.
Problem 1 :
25x2 + 9y2 - 36y - 189 = 0
Problem 2 :
-2x2 + 20x + y - 44 = 0
Problem 3 :
-y2 + 2x + 2y + 3 = 0
Problem 4 :
16x2 + 9y2 - 16x + 18y - 131 = 0
Problem 5 :
x2 + y2 - 8x + 8y + 31 = 0
Problem 6 :
2x2 + 2y2 - 14x - 2y + 7 = 0
Answer Key
1) Ellipse
2) Parabola
3) Parabola
4) Ellipse
5) Circle
6) Circle
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