JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(P : y ^{2}=4 a x , a>0\) be a parabola with focus \(S\).Let the tangents to the parabola \(P\) make an angle of \(\frac{\pi}{4}\) with the line \(y=3 x+5\) touch the parabola \(P\) at \(A\) and \(B\). Then the value of \(a\) for which \(A , B\) and \(S\) are collinear is
- A \(8\) only
- B \(2\) only
- C \(\frac{1}{4}\) only
- D any \(a > 0\)
Answer & Solution
Correct Answer
(D) any \(a > 0\)
Step-by-step Solution
Detailed explanation
Lines making angle \(\frac{\pi}{4}\) with \(y=3 x+5\) have slope \(-2\) and \(1 / 2\). Which are perpendicular to each-other so, \(A, S, B\) are collinear for all \(a >0\).
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