Question 673196
Write the standard equation for each Hyperbola.
vertices ( 0, -12) ( 0, 12) and co-vertices (-11, 0) (11, 0)
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This is a hyperbola with vertical transverse axis.
Its standard form of equation:{{{(y-k)^2/a^2-(x-h)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center.
For given hyperbola:
center: (0,0) (midpoints of horizontal conjugate axis and vertical transverse axis)
length of vertical transverse axis=24 (-12 to 12)=2a
a=12
a^2=144
length of horizontal conjugate axis=22 (-11 to 11)=2b
b=11
b^2=121
Equation of given hyperbola:
{{{y^2/144-x^2/121=1}}}