Find the center foci and vertices of the ellipse Graph the e

Find the center, foci, and vertices of the ellipse. Graph the equation. 25x2 +36y? 250x-360y 625 0 Type the coordinates of the center of the ellipse in the boxes below. Type the coordinates of the vertices in the boxes below. Vertex right of ce Vertex left of center (Simplify your a Type the coordinates of the foci in the boxes below. Focus right of center Focus left of center LL) (Simplify your answers.) Which graph shovn below is the graph of the ellipse O A. OB. OC. O D.

Solution

25x^2 + 36y^2 +250x -360y + 625 =0

25(x^2 +10x) +36(y^2 -10y) =0

(x+5)^2/36 + (y -5)^2/25 =1

centre ( -5 , 5)

a = 6 ; b = 5

Vertex right centre (-5+6 , 5) = (1 , 5)

Vertex left centre ( -11, 5)

c = sqrt(6^2 - 5^2) = sqrt11

Foci right centre : (-5 +sqrt11, 5)

Foci left centre : ( -5 -sqrt11, 5)

Graph option B