Question 1137157

Find an equation of the ellipse that has
 
-a center ({{{-2}}},{{{5}}})->{{{h=-2}}}, {{{k=5}}}
-a minor axis of length{{{ 10}}}->{{{2b=10}}}->{{{b=5}}}
-and a vertex at ({{{9}}},{{{5}}})


{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}.....plug in {{{h=-2}}},{{{ k=5}}}, and {{{b=5}}}

{{{(x-(-2))^2/a^2+(y-5)^2/5^2=1}}}

{{{(x+2)^2/a^2+(y-5)^2/25=1}}}


 a vertex at ({{{9}}},{{{5}}}), use it to find {{{a^2}}}


{{{(9+2)^2/a^2+(5-5)^2/25=1}}}

{{{11^2/a^2+0/25=1}}}

{{{121=a^2}}}


{{{(x+2)^2/121+(y-5)^2/25=1}}}


{{{drawing ( 600, 600, -15, 15, -15, 15,
circle(9,5,.12),locate(9,5,V(9,5)),
circle(-2,5,.12),locate(-2,5,C(-2,5)),
graph( 600, 600, -15, 15, -15, 15,-sqrt(25(1-(x+2)^2/121))+5 ,sqrt(25(1-(x+2)^2/121))+5)) }}}