Find the equation of the ellipse centered at the origin that satisfies the given conditions: foci on x-axis; x-intercepts +-10 y-intercepts +-5

Given that center is at origin that is (0,0)

x intercepts are + 10 and -10 so the right most and left most points are ( 10,0) and (-10,0)

the y intercepts are + 5 and -5 so the top most point is (0,5 ) and bottom most point is ( 0,-5 )

now we find half of major length ( which is along x axis here )= (10+10 )/2=10

and half of minor length ( which is along y axis here )= (5+5)/2 = 5

hence equation of ellipse : ( X - 0 ) ^2 + ( Y -0 )^2

10 ^2 5 ^2

this is a free response question but the answer would be ( X - 0 ) ^2 + ( Y -0 )^2