Find an Equation for the Ellipse Whose Foci Are$( \pm 3,0 )$

Question

Examlex · Accepted Answer

The Answer is

c = 3

, since the fociare

( \pm 3,0 )

, and

a = 4

since the vertices are

( \pm 4,0 )

, so

b ^ { 2 } = a ^ { 2 } - c ^ { 2 } = 7

The major axis is horizontal, so the equation of the ellipse is

\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 \Leftrightarrow \frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 7 } = 1

Find an Equation for the Ellipse Whose Foci Are $( \pm 3,0 )$