JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(P (3,3)\) be a point on the hyperbola, \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 .\) If the normal to it at \(P\) intersects the \(x\)-axis at \((9,0)\) and \(e\) is its eccentricity, then the ordered pair \(\left( a ^{2}, e ^{2}\right)\) is equal to
- A \(\left(\frac{9}{2}, 3\right)\)
- B \(\left(\frac{9}{2}, 2\right)\)
- C \(\left(\frac{3}{2}, 2\right)\)
- D \((9,3)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{9}{2}, 3\right)\)
Step-by-step Solution
Detailed explanation
since, (3,3) lies on \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) \(\frac{9}{a^{2}}-\frac{9}{b^{2}}=1\) Now, normal at (3,3) is \(y-3=-\frac{a^{2}}{b^{2}}(x-3)\) which passes through \((9,0) \Rightarrow b ^{2}=2 a ^{2} \quad \ldots .(2)\) So,…
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