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

1 Answer
Alan P.
Dec 12, 2016

color(green)((y-0)^2/(2^2)-(x-0)^2/(12^2)=1

Explanation:

The standard form for a hyperbola is
either
color(white)("XXX")(x-h)^2/(a^2)-(y-k)^2/(b^2)=1 for a hyperbola opening left-right
or
color(white)("XXX")(y-k)^2/(b^2)-(x-a)^2/(a^2)=1 for a hyperbola opening up-down.
In both cases the center is at (h,k)

Given
color(white)("XXX")y^2-x^2/36=4
we obviously will need to transform this into the second (up-down opening) form.

color(white)("XXX")y^2/4-x^2/(4 * 36) =1

color(white)("XXX")y^2/2^2 - x^2/(12^2)=1

or (if you wish to make the center explicit)
color(white)("XXX")(y-0)^2/(2^2)-(x-0)^2/(12^2)=1

While, not technically in "standard form", this could be simplified as:
color(white)("XXX")y^2/4-x^2/144=1

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