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Identify the type of conic, if any, represented by this equation

0 votes

x^2 - 6x -4y^2 +12y -5=0?

 
A) Parabola
B) Ellipse
C) Circle
D) Hyperbola

 

asked Jul 20, 2014 in PRECALCULUS by anonymous

1 Answer

0 votes

The equation is x2 - 6x - 4y2 +12y - 5 = 0.

x2 - 6x - 4y2 +12y = 5

Add and subtract 9 to form perfect square.

x2 - 6x+ 9 - 4y2 +12y - 9 = 5

(x - 3)2 - 4(y2 - 3y - 9/4) = 5

(x - 3)2 - 4(y - 3/2)2 = 5

Divide each side by 5.

(x - 3)2 /5 - 4(y - 3/2)2 /5 = 1

(x - 3)2 /5 - (y - 3/2)2 /(5/4) = 1

The above equation is in the form form hyperbolic equation (x - h)2 /a2 - (y - k)2 /b2 = 1.

Therefore the answer is D.

answered Jul 20, 2014 by joly Scholar

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