Question 1137164

Find an equation of the ellipse that has

-a center ({{{5}}},{{{-4}}})->{{{h=5}}}, {{{k=-4}}}
-a minor axis of length{{{ 8}}}->{{{2b=8}}}->{{{b=4}}}
-and a vertex at ({{{0}}},{{{-4}}})


{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}.....plug in {{{h=5}}},{{{ k=-4}}}, and {{{b=4}}}

{{{(x-5)^2/a^2+(y-(-4))^2/4^2=1}}}

{{{(x-5)^2/a^2+(y+4)^2/16=1}}}


 a vertex at ({{{0}}},{{{-4}}}), use it to find {{{a^2}}}


{{{(0-5)^2/a^2+(-4+4)^2/16=1}}}

{{{25/a^2+0/16=1}}}

{{{25=a^2}}}


{{{(x-5)^2/25+(y+4)^2/16=1}}}


{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(0,-4,.12),locate(0,-4,V(0,-4)),
circle(5,-4,.12),locate(5,-4,C(5,-4)),
graph( 600, 600, -10, 10, -10, 10,-sqrt(16(1-(x-5)^2/25))-4 ,sqrt(16(1-(x-5)^2/25))-4)) }}}