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P 1 and P 2 are corresponding points on the ellipse x 2 16 + y 2 9 = 1 and its auxiliary circle respectively. If the normal at P 1 to the ellipse meets O P 2 in Q (where O is the origin), then the length of O Q is equal to

Options

  1. A3 units
  2. B9 units
  3. C4 units
  4. D7 units

Correct answer

D. 7 units

Step-by-step solution

Let, P 1 = 4 cos ⁡ θ , 3 sin ⁡ θ and P 2 = 4 cos ⁡ θ , 4 sin ⁡ θ Now, equation of P 1 Q is 4 x cos ⁡ θ - 3 y sin ⁡ θ = 7 Equation of P 2 Q is x cos ⁡ θ = y sin ⁡ θ Q = 7 cos ⁡ θ , 7 sin ⁡ θ ⇒ O Q = 7

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