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 and Q be the points (1, 2) and (2, 1) respectively. Then

• 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 outside E

Answer 1

The given ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$. The value of the expression $\frac{x^{2}}{9} + \frac{y^{2}}{4} - 1$is positive for $x = 1,y = 2$and negative for $x = 2,y = 1$. Therefore P lies outside E and Q lies inside E. The value of the expression $x^{2} + y^{2} - 9$is negative for both the points P and Q. Therefore P and Q both lie inside C. Hence P lies inside C but outside E