Question 1204632
<br>
The center is given as (3,-2).<br>
Two points on the ellipse are (-4,-2) and (10,-2); each of those is 7 units horizontally from the center.<br>
Two other points are (3,1) and (3,-5); each of those is 3 units vertically from the center.<br>
So the ellipse has a horizontal semi-major axis of length 7 and a vertical semi-minor axis of length 3.<br>
Given that information, the equation in standard form is<br>
{{{(x-3)^2/7^2+(y+2)^2/3^2=1}}}<br>
{{{(x-3)^2/49+(y+2)^2/9=1}}}<br>
Convert to general form by multiplying by (9*49=441), expanding the expressions in parentheses, and simplifying.<br>
{{{9(x-3)^2+49(y+2)^2=441}}}
{{{9(x^2-6x+9)+49(y^2+4y+4)=441}}}
{{{9x^2-54x+81+49y^2+196y+196=441}}}
{{{9x^2+49y^2-54x+196y=164}}} or {{{9x^2+49y^2-54x+196y-164=0}}}<br>