WBJEE · Maths · Hyperbola
Let \(P(4,3)\) be a point on the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=\mathrm{1}\). If the normal at \(P\) intersects the \(X\) -axis at (16,0) , then the eccentricity of the hyperbola is
- A \(\frac{\sqrt{5}}{2}\)
- B 2
- C \(\sqrt{2}\)
- D \(\sqrt{3}\)
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Given hyperbola equation \(H: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) \(P(4,3) \) lie on \(H\) \(\Rightarrow\) \(\frac{16}{a^{2}}-\frac{9}{b^{2}}=1\) Normal equation at \(P(4,3)\) for \(H\) \[ a^{2} y_{1}\left(x-x_{1}\right)+b^{2} x_{1}\left(y-y_{1}\right)=0 \]…
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