Question

What is the equation of the ellipse whose vertices are $(\pm 5,0)$ and foci are at $(\pm 4,0)$?

• A. $\frac{x^2}{25}+\frac{y^2}{9}=1$
• B. $\frac{x^2}{16}+\frac{y^2}{9}=1$
• C. $\frac{x^2}{25}+\frac{y^2}{16}=1$
• D. $\frac{x^2}{9}+\frac{y^2}{25}=1$

Answer 1

The correct option is A $\frac{x^2}{25}+\frac{y^2}{9}=1$

$Vertices=(\pm 5,0)$

$focii=(\pm 4,0)$

Major axis is along X-axis

Equation of Ellipse $\to \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Given $\to a=5$

Now we know that $focii=(\pm c,0)$

and $c^2=a^2-b^2$

$\therefore 16=25-b^2\to b^2=25-16$

$\to b^2=9\to b=(\pm 3,0)$

$\therefore$ Equation of Ellipse $=\frac{x^2}{25}+\frac{y^2}{9}=1$.