Question

given the following equation for an ellipse: 9x^2+25y^2-18x-50y-191=0
write the equation in standard form and graph the ellipse.
(label the center and 4 points)(show details please!)

Answer 1

$9x^2+25y^2-18x-50y-191=0\\

\therefore 9(x^2-2x+1)+25(y^2-2y+1)-191 -9-25=0\\

9(x-1)^2+25(y-1)^2=225\\

\therefore \text{Center=(1,1)}\\

\text{Let new x and y be X and Y}\\

\implies X=x-1 \:;\: Y=y-1\\

\implies \frac{X^2}{5^2}+ \frac{Y^2}{3^2}=1$

That's the equation in the standard form, with center as the origin and axes parallel to the coordinate axes.