Question

What is the equation of the ellipse with foci at (5, 0), (-5, 0) and vertices (9, 0), (-9, 0)?

Answer 1

Answer: $\dfrac{x^2}{81}+\dfrac{y^2}{56}=1$

Step-by-step explanation:

General equation of ellipse : $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}$

Given: Vertices of ellipse : (± 9,0)

Since the vertices are of the form (± a, 0).

i.e. a=9

Thus, the major axis is along x-axis.

Also, foci of the ellipse = (±5,0)

Since, foci is of the form (± c,0), i.e. c=5

Since

$c^2=a^2-b^2\\\\\Rightarrow\ 5^2= 9^2-b^2\\\\\Rightarrow\ b^2=81-25\\\\\Rightarrow\ b^2=56$

Equation of ellipse :

$\dfrac{x^2}{9^2}+\dfrac{y^2}{56}=1\\\\\Rightarrow\ \dfrac{x^2}{81}+\dfrac{y^2}{56}=1$

Hence, the required equation : $\dfrac{x^2}{81}+\dfrac{y^2}{56}=1$