JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 13 April 2023, Shift 1, Maths Q26

Question 26 of 90 in this shift, Maths question 26 of 30, Section B.

Let

m_1

and

m_2

be the slopes of the tangents drawn from the point P(4, 1) to the hyperbola

H:\frac{y^2}{25}-\frac{x^2}{16}=1

. If Q is the point from which the tangents drawn to H have slopes

|m_1|

and

|m_2|

and they make positive intercepts

\alpha

and

\beta

on the

x

-axis, then

\frac{(PQ)^2}{\alpha\beta}

is equal to ________.

Official answer

NTA final key.