First slide

Ellipse

Question

Let $E$ be the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ and $C$ be the circle
$x^{2} + y^{2} = 9 .$ Let $P (1, 2)$ and $Q (2, 1)$ be two points, then

Moderate

A

$Q$ lies inside $C$ but outside $E$
B

$Q$ lies outside both $C$ and $E$
C

$P$ lies inside both $C$ and $E$
D

$P$ lies inside $C$ but out side $E$

Solution

$C : x^{2} + y^{2} - 9 = 0$
$E : x^{2} / 9 + y^{2} / 4 - 1 = 0$
.

For $P (1, 2), C : 1 + 4 - 9 < 0, E : \frac{1}{9} + \frac{4}{4} - 1 > 0$
So $P$ lies outside $E$ and inside $C .$
For $Q (2, 1), C : 4 + 1 - 9 < 0, E : \frac{4}{9} + \frac{1}{4} - 1 < 0$
So $Q$ lies inside both $C$ and $E$ .

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App