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If m 1 and m 2 are the slopes of the tangents to the ellipse x 2 16 + y 2 9 = 1 which passes through 5,4 , then the value of m 1 + m 2 - m 1 m 2 is equal to

Options

  1. A47 9
  2. B- 40 9
  3. C22 3
  4. D11 3

Correct answer

D. 11 3

Step-by-step solution

Let the equation of tangent passing through 5,4 is y = m x ± 16 m 2 + 9 ⇒ 4 = 5 m ± 16 m 2 + 9 ⇒ 4 - 5 m 2 = 16 m 2 + 9 ⇒ 9 m 2 - 40 m + 7 = 0 ⇒ m 1 + m 2 = 40 9 , m 1 m 2 = 7 9 ⇒ m 1 + m 2 - m 1 m 2 = 33 9 = 11 3

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