Question

How do you write a standard form equation for the hyperbola with `9x^2 – y^2 – 36x + 4y + 23 = 0`?

Answer 1

`(x-2)^2 /1^2 - (y-2)^2/ 3^2 =1`

Explanation:

Rewrite, the equation as follows:

`9(x^2 -4x) -(y^2 -4y) +23=0`

`9(x^2-4x+4) -(y^2 -4y +4) -36 +4+23=0`

#9(x-2)^2 - (y-2)^2 = 9

`(x-2)^2 /1^2 - (y-2)^2/ 3^2 =1`