Question 1136097
Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ± (5/4)x.

The equation of this hyperbola in standard form:

{{{y^2 / a^2 - x^2 / b^2 = 1}}}

{{{y }}}= ±{{{( a/b )x}}}

±{{{(5/4)x }}}= ±{{{( a/b )x}}}

{{{a / b = 5 / 4}}}

{{{a = 10}}}

{{{10 / b = 5 / 4}}}

{{{b = (10*4)/5}}}

{{{b = 8}}}


The equation of the hyperbola is:

{{{y^2 / 10^2 - x^2/ 8^2 = 1}}}

{{{y^2 / 100 - x^2/ 64 = 1}}}



{{{ graph( 600, 600, -35, 35, -35, 35,-sqrt(100(x^2/ 64+1)) ,sqrt(100(x^2/ 64+1))) }}}