JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the line \(x-1=0\), is a directrix of the hyperbola \(kx ^{2}- y ^{2}=6\), then the hyperbola passes through the point.
- A \((-2 \sqrt{5}, 6)\)
- B \((-\sqrt{5}, 3)\)
- C \((\sqrt{5},-2)\)
- D \((2 \sqrt{5}, 3 \sqrt{6})\)
Answer & Solution
Correct Answer
(C) \((\sqrt{5},-2)\)
Step-by-step Solution
Detailed explanation
\(frac{x^{2}}{6 / k }-\frac{y^{2}}{6}=1\) \(e ^{2}=1+\frac{6}{6 / k }\) \(e =\sqrt{1+ k }\) \(a =\sqrt{\frac{6}{ k }}\) Eq. of directrix \(x=\frac{a}{e} \Rightarrow x=\sqrt{\frac{6}{k(k+1)}}\) \(\frac{6}{k(k+1)}=1\) \(k=2\) From eq.\((1)\), we get \(2 x^{2}-y^{2}=6\) Check…
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