JEE PYQ: Ellipse Question 23
Question 23 - 2019 (12 Apr Shift 2)
An ellipse, with foci at $(0, 2)$ and $(0, -2)$ and minor axis of length 4, passes through which of the following points?
(a) $(\sqrt{2}, 2)$ (b) $(2, \sqrt{2})$ (c) $(2, 2\sqrt{2})$ (d) $(1, 2\sqrt{2})$
Show Answer
Answer: (a) $(\sqrt{2}, 2)$
Solution
Minor axis $= 2a = 4 \Rightarrow a = 2$, $be = 2$
$a^2 = b^2(1 - e^2) \Rightarrow 4 = b^2 - 4 \Rightarrow b = 2\sqrt{2}$
Ellipse: $\frac{x^2}{4} + \frac{y^2}{8} = 1$
$(\sqrt{2}, 2)$: $\frac{2}{4} + \frac{4}{8} = 1$ satisfies.
BETA
