JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(\lambda x-2 y=\mu\) be a tangent to the hyperbola \(a^{2} x^{2}-y^{2}=b^{2}\). Then \(\left(\frac{\lambda}{a}\right)^{2}-\left(\frac{\mu}{b}\right)^{2}\) is equal to
- A \(-2\)
- B \(-4\)
- C \(2\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\(\lambda x -2 y =\mu\) is a tangent to the curve \(a^{2} x^{2}-y^{2}=b^{2}\) then \(a ^{2} x ^{2}-\left(\frac{\lambda x -\mu}{2}\right)^{2}= b ^{2}\) \(\left(4 a ^{2}-\lambda^{2}\right) x ^{2}+2 \lambda \mu x -\mu^{2}-4 b ^{2}=0\) Disc. \(=0\)…
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