Find equation of asymptote, verticies, write equation in standard form, etc.

Question

The general form of the equation of a hyperbola is (x^2)-(y^2)-14x-8y+29=0. Write the equation of this hyperbola in standard form and give the coordinates of the center, the coordinates of the verticies, and the equations of the asymptotes. Then graph the hyperbola.

Answer 1

Hi Lilly,

 

x²-y²-14x-8y+19=0

<=>(x²-14x+49)-(y²-8y+16)+19-16-49=0, I just added and subtracted 16 & 49 to complete the squares

<=>(x-7)²- (x-4)² = 46

         46         46       46

 

<=>(x-7)² - (y-4)² = 1

         46         46
 Asymptote is given by the equation y - k = +/-(b/a)(x - h)

a = b = 46, h = 7, k = 4

I hope this helps