JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(a\) and \(b\) respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation \(9e^2 - 18e + 5 = 0.\) If \(S(5, 0)\) is a focus and \(5x = 9\) is the corresponding directrix of this hyperbola, then \(a^2 - b^2\) is equal to
- A \(-7\)
- B \(-5\)
- C \(5\)
- D \(7\)
Answer & Solution
Correct Answer
(A) \(-7\)
Step-by-step Solution
Detailed explanation
\(S\left( {5,0} \right)\,\) is focus \( \Rightarrow ae = 5\) (focus) ......\((1)\) \(x = \frac{a}{5} \Rightarrow \frac{a}{e} = \frac{9}{5}\) (directrix) .....\((2)\) \(\left( 1 \right) \left( 2 \right) \Rightarrow {a^2} = 9\)…
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