JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let the circle \(C\) touch the line \(x-y+1=0\), have the centre on the positive x -axis, and cut off a chord of length \(\frac{4}{\sqrt{13}}\) along the line \(-3 x+2 y=1\). Let H be the hyperbola \(\frac{x^2}{\alpha^2}-\frac{y^2}{\beta^2}=1\), whose one of the foci is the centre of \(C\) and the length of the transverse axis is the diameter of \(C\). Then \(2 \alpha^2+3 \beta^2\) is equal to ______
- A 17
- B 18
- C 19
- D 20
Answer & Solution
Correct Answer
(C) 19
Step-by-step Solution
Detailed explanation
\(r=\left|\frac{a+1}{\sqrt{2}}\right| \Rightarrow(a+1)^2=2 r^2\) Also \(\left(\frac{3 a-1}{\sqrt{13}}\right)^2+\left(\frac{2}{\sqrt{13}}\right)^2=r^2\)…
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