Question

Find the equation of the ellipse in standard form whose Foci is (2,7) and (-2,7) and the length of the major axis is 6

Answer 1

The center is located midway between the vertices on the major axis:

center=$(\frac{(2+(-2)}{2},\frac{7+7}{2})=(0,7)$

length of major axis= 6=2a

$\implies a=3$

$c^2=a^2-b^2\\ c=2,a=3\\ 2^2=3^2-b^2\\ b^2=9-4=5\\ b=\sqrt 5$

The standard form equation of the ellipse is $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

$\frac{x^2}{9}+\frac{(y-7)^2}{5}=1$