JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Consider the circle \(\mathrm{C}: \mathrm{x}^2+\mathrm{y}^2=4\) and the parabola \(P: y^2=8 x\). If the set of all values of \(\alpha\), for which three chords of the circle \(\mathrm{C}\) on three distinct lines passing through the point \((\alpha, 0)\) are bisected by the parabola \(P\) is the interval \((p, q)\), then \((2 q-p)^2\) is equal to .............
- A \(80\)
- B \(70\)
- C \(90\)
- D \(10\)
Answer & Solution
Correct Answer
(A) \(80\)
Step-by-step Solution
Detailed explanation
\( T=S_1 \) \( x_1+y y_1=x_1^2+y_1^2 \) \( \alpha x_1=x_1^2+y_1^2 \) \( \alpha\left(2 t^2\right)=4 t^4+16 t^2 \) \( \alpha=2 t^2+8 \) \( \frac{\alpha-8}{2}=t^2\) Also, \(4 \mathrm{t}^4+16 \mathrm{t}^2-4<0\) \( \mathrm{t}^2=-2+\sqrt{5} \) \( \alpha=4+2 \sqrt{5} \)…
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