Question

The ellipse with foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3)

Answer 1

Given foci (4,0) and (-4,0)

 Horizontal ellipse equation is x^2/a^2+y^2/b^2 = 1.

center of ellipse is at (0,0)

major axis (c,0),(-c,0)

Given y intercepts of ellipse is end points of the minor axis (0,b),(0,-b)

x intercepts of ellipse end points of (a,0),(-a,0)

c^2 = a^2-b^2

4^2 = a^2-3^2

16 = a^2-9

16+9 = a^2

25 = a^2

Required ellipse equation is x^2/25+y^2/9 = 1