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 π 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:

Question

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 π 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:, 8 only, 2 only, 1 4 only, any a > 0

MARKS App · Accepted Answer

Lines making angle π 4 with y = 3 x + 5 So using formula tan α = m 2 - m 1 1 + m 1 m 2 , we have slope - 2 & 1 2 . Which are perpendicular to each-other so, A , S , B are collinear for all a > 0 . (by property that perpendicular tangents will lie on directrix and chord of contact will pass through focus, so the points are collinear )

Search any question & find its solution

Looking for more such questions to practice?