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

Question

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

 

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

 

Answer 1

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.