JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let a line \(L_{1}\) be tangent to the hyperbola \(\frac{x^{2}}{16}-\frac{y^{2}}{4}=1\) and let \(L_{2}\) be the line passing through the origin and perpendicular to \(L _{1}\). If the locus of the point of intersection of \(L_{1}\) and \(L_{2}\) is \(\left(x^{2}+y^{2}\right)^{2}=\) \(\alpha x^{2}+\beta y^{2}\), then \(\alpha+\beta\) is equal to
- A \(11\)
- B \(12\)
- C \(15\)
- D \(16\)
Answer & Solution
Correct Answer
(B) \(12\)
Step-by-step Solution
Detailed explanation
\(\frac{x \sec \theta}{4}-\frac{y \tan \theta}{2}=1\) \(m_{1}=\frac{\sec \theta \times 2}{4(\tan \theta)}=\frac{\sec \theta}{2 \tan \theta}\) \(m_{2}=\frac{k}{h}\) \(m_{1} m_{2}=-1\) \(\frac{ k }{ h } \frac{\sec \theta}{2 \tan \theta}=-1\) \(\frac{ k }{2 h \sin \theta}=-1\)…
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