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If θ is the angle between the pair of tangents drawn to the ellipse 3 x 2 + 2 y 2 = 5 from the point 1,2 , then the value of tan 2 θ is equal to

Correct answer

28.8

Step-by-step solution

The equation of the tangent to 3 x 2 + 2 y 2 = 5 in slope form is y = m x ± 5 3 m 2 + 5 2 If it passes through 1,2 , then 2 - m 2 = 5 3 m 2 + 5 2 ⇒ 2 m 2 3 + 4 m - 3 2 = 0 ⇒ m 1 + m 2 = - 4 2 3       &         m 1 m 2 = - 3 2 2 3 ⇒ m 1 + m 2 = - 6       &         m 1 m 2 = - 9 4 tan ⁡ θ = m 1 + m 2 2 - 4 m 1 m 2 1 + m 1 m 2 t a n 2 θ = 36 + 9 - 5 4 2 = 45 × 16 25 = 144 5 = 28.8

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