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Given the ellipse E   4 x 2 + 9 y 2 - 36 = 0 , the circle C   x 2 + y 2 - 9 = 0 and two points A ( 1 ,   2 ) ,   B ( 2 ,   1 ) , which of the following is correct?

Options

  1. AB lies inside C but outside E
  2. BB lies outside both C and E
  3. CA lies inside both C and E
  4. DA lies inside C , but outside E

Correct answer

D. A lies inside C , but outside E

Step-by-step solution

Given the ellipse E ≡ 4 x 2 + 9 y 2 - 36 = 0 . . . . . . . . . . . . . . . . . . . . . . i the circle C ≡ x 2 + y 2 - 9 = 0 . . . . . . . . . . . . . . . . . . . . . . . . i i and two points A x 1 , y 1 ≡ ( 1 ,   2 ) ,   B x 2 , y 2 ≡ ( 2 ,   1 ) Now, E 1 ≡ 4 x 1 2 + 9 y 1 2 - 36 = 4 1 2 + 9 2 2 - 36 = 4 > 0 So A lies outside E . E 2 ≡ 4 x 2 2 + 9 y 2 2 - 36 = 4 2 2 + 9 1 2 - 36 = - 11 < 0 So B lies inside E . C 1 ≡ x 1 2 + y 1 2 - 9 = 1 2 + 2 2 - 9 =

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