Question 975218
Write the equation of an hyperbola, in standard form, with vertices ( 0,3) and (0,-3) and asymptotes y=3/2x and y=-3/2x
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Given hyperbola has a vertical transverse axis.
Its standard form of equation: {{{(y-k)^2/a^2-(x-h)^2/b^2=1}}}, (h,k)=coordinates of center
center: (0, 0)
vertices:
a=3
a^2=9
Given slopes of asymptotes with vertical transverse axis=a/b=±3/2
b=2a/±3
b^2=4a^2/9
b^2=4*9/9=4
equation: {{{y^2/9-x^2/4=1}}}