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

1 Answer
Dec 12, 2016

Answer:

#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#