Question

How do you write the hyperbola `36y^2-4x^2=9` in standard form?

Answer 1

`y^2/(1/4)-x^2/(9/4)=1`

Explanation:

Write `36y^2-4x^2 =9` in standard form.

Standard form of a hyperbola with a positive `y^2` term and a negative `x^2` term is `frac[(y-k)^2}{a^2}-frac{(x-h)^2}{b^2}=1` where `(h,k)` is the center.

Divide the equation by 9 to obtain a 1 on the right side.

`(36y^2)/9 -(4x^2)/9=9/9`

`4y^2-4/9 x^2=1`

Divide each term on the left side by the reciprocal of the coefficient.

`y^2/(1/4)-x^2/(9/4)=1`

In this example, `(h,k) = (0,0)`