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

1 Answer
Shell
Dec 1, 2016

#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)#

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