Let the tangents PQ and PR are drawn to y^2=4ax from any point P on the line x+4a=0. The angle subtended by the chord of contact QR at the vertex of…

Question

Let the tangents PQ and PR are drawn to y^2=4ax from any point P on the line x+4a=0. The angle subtended by the chord of contact QR at the vertex of the parabola y^2=4ax is

MARKS Content Team · Accepted Answer

Correct answer: (C) (π)/2. Let, Q=at12,2at_1 and R=at22,2at_2, then P=at_1t_2,at_1+t_2 which lies on x+4a=0 ⇒at_1t_2=-4a⇒t_1t_2=-4 Now, the vertex of the parabola y^2=4ax is the origin O0,0 ⇒slope of OQ=2t_1 & slope of OR=2/t_2 ⇒2/t_1×2/t_2=4/t_1t_2=4/(-4)=-1 ⇒OQ is perpendicular to OR ⇒∠QOR=90^(∘)=(π)/2

Let the tangents $P Q$ and $P R$ are drawn to $y^{2} = 4 a x$ from any point $P$ on the line $x + 4 a = 0 .$ The angle subtended by the chord of contact $Q R$ at the vertex of the parabola $y^{2} = 4 a x$ is

Solution

More Parabola Questions

Let the tangents PQ and PR are drawn to y2=4ax from any point P on the line x+4a=0. The angle subtended by the chord of contact QR at the vertex of the parabola y2=4ax is

Solution

More Parabola Questions

Let the tangents $P Q$ and $P R$ are drawn to $y^{2} = 4 a x$ from any point $P$ on the line $x + 4 a = 0 .$ The angle subtended by the chord of contact $Q R$ at the vertex of the parabola $y^{2} = 4 a x$ is