Question

An ellipse, with foci at $(0,2)$ and $(0,–2)$ and minor axis of length $4$, passes through which of the following points ?

• A. $(2,\sqrt{2})$
• B. $(1,2\sqrt{2})$
• C. $(\sqrt{2},2)$
• D. $(2,2\sqrt{2})$

Answer 1

The correct option is C $(\sqrt{2},2)$

Foci are $(0,2)$ and $(0,–2)$
So, major axis is $y$-axis.
Let the equation of ellipse be $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$

Given, $2b=4$ and $2c=4$
$\Rightarrow b=2,c=2$
$\Rightarrow c^2=4\Rightarrow a^2-b^2=4\Rightarrow a^2=8$
Therefore, equation of the ellipse is $\frac{x^2}{4}+\frac{y^2}{8}=1$
By putting all the points, we get that $(\sqrt{2},2)$ lies on the ellipse.