# CONVERTING THE GIVEN EQUATION OF CONICS TO THE STANDARD FROM WORKSHEET

Convert the equation to standard form by completing the square. Then identify what type of conic section the equation represents.

If it is a circle, ellipse, or hyperbola, then name its center. If it is a parabola, then name its vertex.

Problem 1 :

x2 + 6x + 8y + 1 = 0

Solution

Problem 2 :

9y2 - 4x2 - 18y + 24x - 63 = 0

Solution

Problem 3 :

4x2 + 36y - 32x + 9y2 + 64 = 0

Solution

Problem 4 :

9x2 + 16y2 - 18x + 64y - 71 = 0

Solution

Problem 5 :

4x2 - y2 + 32x + 6y + 39 = 0

Solution

Problem 6 :

x2 + y2 - 6x + 8y = 1

Solution

Problem 7 :

4x2 + 4y2 - 24x + 32y - 4 = 0

Solution

Problem 8 :

y2 + 8y - 4x + 8 = 0

Solution

 1 Parabola (x + 3)2 = -8(y - 1)Vertex (-3, 1) 2 Hyperbola (x-h)2a2-(y-k)2b2=1 Center (3, 1) 3 Ellipse (x-h)2a2+(y-k)2b2=1 Center (4, -2) 4 Ellipse (x-h)2a2+(y-k)2b2=1 Center (1, -2) 5 Hyperbola (x-h)2a2-(y-k)2b2=1 Center (-4, 3) 6 Circle (x - 3)2 + (y + 4)2 = 26Center (3, -4) 7 Circle (x - 3)2 + (y + 4)2 = 26Center (3, -4) 8 Hyperbola (y + 4)2 = 4(x + 2)Center (-2, -4)

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