ParabolaHard
Question
If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x1, y1) and (x2, y2) respectively, then -
Options
A.x1 = x2
B.x1 = y2
C.y1 = y2
D.x2 = y1
Solution
Since line passing through focus so t1 t2 = - 1
Point of intersection of tangent at P & Q are
(at1t2, a (t1 + t2))
Point of intersection of normal at P & Q
are (a(t12 + t22 + t1 t2 + 2)), - at1 t2 (t1 + t2)
(x1, y1) = (- a, a (t1 + t2))
(x2, y2) = (a(t + t22 - 1), a(t1 + t2))
⇒ y1 = y2
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