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JEE Main202226 Jul 2022Evening ShiftMathematicsEllipseActual

The acute angle between the pair of tangents drawn to the ellipse 2 x 2 + 3 y 2 = 5 from the point 1 , 3 is

Options

  1. Atan - 1 16 7 5
  2. Btan - 1 24 7 5
  3. Ctan - 1 32 7 5
  4. Dtan - 1 3 + 8 5 35

Correct answer

B. tan - 1 24 7 5

Step-by-step solution

Let equation of tangents to the ellipse x 2 5 2 + y 2 5 3 = 1 be y = m x ± 5 2   m 2 + 5 3 Since the tangents pass through 1 , 3 , so 3 = m ± 15 m 2 + 10 6 ⇒ 9 m 2 + 36 m - 44 = 0 Let θ be the angle between the tangents, so tan θ = m 1 - m 2 1 + m 1   m 2 i.e. tan θ = 4 2 + 4 44 9 1 - 44 9 = 24 5 35 ⇒ θ = tan - 1 24 7 5

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