Discussion Forum

1)

Let PQ be a focal chord of the parabola y²=4ax.The tangents to the parabola at P and Q meet at point lying on the line y=2x+a, a >0

 Length  of chord PQ is 

Answer:

Option B

Explanation:

Concept involved

 Intersection point of tangents at  $(at_1^2,2at_{1})$ and $(at_2^2,2at_{2})$ is ( at₁t₂ , a/t₁ +t₂) ) , also tangents drawn  at end point of focal chord are perpendicular and intersect on directrix

 Since  $R\left(-a,a(t-\frac{1}{t})\right)$  lies on y =2x+a

 

$\Rightarrow$    $ a.(t-\frac{1}{t})=-2a+a$

 $\Rightarrow$     $t-\frac{1}{t}=-1$

 Thus, length of focal chord

 $a( t+\frac{1}{t})^{2}=a\left\{\left(t-\frac{1}{t}\right)^{2}+4\right\}=5a$