Paragraph: Let $P Q$ be a focal chord of the parabola $y^{2}=4 a x$. The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y=2 x+a, a0$. Question: Length of chord $P Q$ is

Question

Paragraph: Let $P Q$ be a focal chord of the parabola $y^{2}=4 a x$. The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y=2 x+a, a>0$. Question: Length of chord $P Q$ is

Aicharya · Accepted Answer

R lies on y = 2x + a R , &#160; y &#160; = &#160; 2 x &#160; + &#160; a &#8658; a&#160; t - 1 t = - a t - 1 t = - 1 &#8658; t + 1 t 2 = 1 + 4 = 5 PQ = a&#160; t + 1 t 2 = 5 a

Paragraph: Let $P Q$ be a focal chord of the parabola $y^{2}=4 a x$. The tangents to the parabola at $P$ and…

Solution