Question

find the standard equation of the ellipse when foci (-8, 0) and (8,0), the sum of the distances of any point from the foci is 20

Answer 1

Hi,

Explanation:

Foci are on the x-axis F(-8,0) and F'(8,0), A and A' are vertex on x-axis

d =20

FF'=16

F'A=F'F+FA=16+4=20

A=(12,0) , A'=(-12,0)

B and B' are vertex on y axis.

O is the center of ellipse

F'O²+OB²=F'B² and F'B=20/2=10 => OB=6

Equation of the ellipse:

`{((x)/(12)) }^2 + {((y)/(6)) }^2=1\\`