Question

need  equation of the ellipse with foci (7, 0), (-7, 0) and co-vertices (0, 3), (0, -3)?

Answer 1

Standard equation of horizontal ellipse is (x-h)^2/a^2+(y-k)^2/b^2 = 1

a > b

Covertices

(h,k+b) = (0,3)

(h,k-b) = (0,-3)

Foci (h+c,k) = (0+c,0) = (c,0) = (7,0)

(h-c,k) = (0-c,0) = (-c,0) = (-7,0)

From above values we can able to write c = 7, b = 3

c = √(a^2-b^2)

7 = √(a^2-9)

Squring to each side.

49 = a^2-9

Add 9 to each side.

49+9 = a^2-9+9

58 = a^2

a = √58

Substitue the values in Standard equation of horizontal ellipse.

(x-0)^2/√58^2+(y-0)^2/3^2 = 1

ellipse equation is x^2/58+y^2/9 = 1