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If the normal to the ellipse x 2 25 + y 2 1 = 1 is at a distance p from the origin, then the maximum value of p is

Correct answer

4

Step-by-step solution

Equation of the normal is 5 sec ⁡ θ x - c o s e c θ y = 2 4 So, p = 24 25 sec 2 ⁡ θ + c o s e c 2 θ = 24 36 + 5 tan ⁡ θ - cot ⁡ θ 2 p m a x = 24 6 = 4

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