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\\</p><p>\therefore 9(x^2-2x+1)+25(y^2-2y+1)-191 -9-25=0\\</p><p>9(x-1)^2+25(y-1)^2=225\\</p><p>\therefore \text{Center=(1,1)}\\</p><p>\text{Let new x and y be X and Y}\\</p><p>\implies X=x-1 \:;\: Y=y-1\\</p><p>\implies (X^2)/(5^2)+ (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.