Question

An ellipse with centre at origin passes through the points $(2,2),(1,4)$. Then the length of its major axis is

• A. $2\sqrt{5}$
• B. $3\sqrt{5}$
• C. $5\sqrt{5}$
• D. $4\sqrt{5}$

Answer 1

Answer: (A)

$2\sqrt{5}$

Let the equation of ellipse be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
Since, it passes through $(2,2)$ and $(1,4)$
then $\frac{4}{a^2}+\frac{4}{b^2}=1$ ....(1)
and $\frac{1}{a^2}+\frac{16}{b^2}=1$ .....(2)
Solving (1) and (2), simultaneously
$\frac{1}{a^2}=\frac{1}{5}$
Therefore, $2a=2\sqrt{5}$