JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
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 \(\left| m _1\right|\) and \(\left| m _2\right|\) and they make positive intercepts \(\alpha\) and \(\beta\) on the \(x\) axis, then \(\frac{(P Q)^2}{\alpha \beta}\) is equal to \(............\).
- A \(6\)
- B \(5\)
- C \(8\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(8\)
Step-by-step Solution
Detailed explanation
Equation of tangent to the hyperbola \(\frac{y^2}{a^2}-\frac{x^2}{b^2}=1\) \(y=m x \pm \sqrt{a^2-b^2 m^2}\) passing through \((4,1)\) \(1=4 m \pm \sqrt{25-16 m ^2} \Rightarrow 4 m ^2- m -3=0\) \(\Rightarrow m =1, \frac{-3}{4}\) Equation of tangent with positive slopes…
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