Question

Equation of the ellipse whose foci are $(2,2)$ and $(4,2)$ and the major axis is of length $10$, is

• A. $\frac{{(x+3)}^2}{24}+\frac{{(y+2)}^2}{25}=1$
• B. $\frac{{(x-3)}^2}{24}+\frac{{(y-2)}^2}{25}=1$
• C. $\frac{{(x+3)}^2}{24}+\frac{{(y+2)}^2}{24}=1$
• D. $\frac{{(x-3)}^2}{25}+\frac{{(y-2)}^2}{24}=1$

Answer 1

The correct option is D $\frac{{(x-3)}^2}{25}+\frac{{(y-2)}^2}{24}=1$

Given, foci of an ellipse are $(2,2)$ and $(4,2)$ and major axis is of length $10$.

$\therefore 2ae=2$ and $2a=10$ $\Rightarrow a=5$

$\therefore 2\times 5\times e=2\Rightarrow e=\frac{1}{5}$

$\because b^2=a^2(1-e^2)\Rightarrow b^2=25(1-\frac{1}{25})$

$\Rightarrow b^2=24$

Centre of ellipse $=$ Mid-point of foci
$=(\frac{2+4}{2},\frac{2+2}{2})=(3,2)$

Hence, equation of ellipse is
$\frac{{(x-3)}^2}{25}+\frac{{(y-2)}^2}{24}=1$