Question

Let E be the ellipse$\frac{x^{2}}{9}$+$\frac{y^{2}}{4}$= 1 and C be the circle centered at (0, 0) with radius 3. Let P and Q be the points (1, 2) and (2, 1) respectively then-

• A. Q lies outside C and E
• B. P lies inside both C and E
• C. P lies inside C but outside E
• D. Q lies inside C but outside E

Answer 1

Answer: (C)

P lies inside C but outside E

Answer 2

E_P = $\frac{1^{2}}{9}$+ $\frac{2^{2}}{4}$– 1 > 0 ̃ P lies outside E

E_Q = $\frac{2^{2}}{9}$+ $\frac{1^{2}}{4}$– 1 < 0 ̃ Q lies inside E

C º x² + y² – 9 = 0

Now

C_P = 1² + 2² – 9 < 0 ̃ P lies inside C

C_Q = 2² + 1² – 9 < 0 ̃ Q lies inside C