Question 1204632


Write the equation for the ellipse in standard form and general form.

{{{(x-h)^2/a^2 +(y-k)^2/b^2=1}}}

given:

center ({{{3}}},{{{-2}}})=({{{h}}},{{{k}}})


so far, equation is:

{{{(x-3)^2/a^2 +(y+2)^2/b^2=1}}}


passing through ({{{-4}}},{{{-2}}}), ({{{10}}},{{{-2}}}), ({{{3}}},{{{1}}}), and ({{{3}}},{{{-5}}})

use two points to calculate {{{a}}} and {{{b}}}

 ({{{3}}},{{{1}}}) 

{{{(3-3)^2/a^2 +(1+2)^2/b^2=1}}}

{{{(0)^2/a^2 +3^2/b^2=1}}}

{{{9/b^2=1}}}

{{{9=b^2}}}

{{{b=3}}}


and ({{{10}}},{{{-2}}})


{{{(10-3)^2/a^2 +(-2+2)^2/9=1}}}

{{{7^2/a^2 +(0)^2/9=1}}}

{{{49/a^2 =1}}}

{{{a^2 =49}}}

{{{a=7}}}


equation is:

{{{(x-3)^2/49 +(y+2)^2/9=1}}}


{{{ drawing( 600, 600, -10, 10, -10, 10,circle(3,-2,.12), locate(3,-2,C(3,-2)),
graph( 600, 600, -10, 10, -10, 10, (1/7)(-3sqrt(-x^2+6x+40)-14), (1/7)(3sqrt(-x^2+6x+40)-14))) }}}