Question

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

• A. 2a
• B. 7a
• C. 5a
• D. 3a

Answer 1

The correct option is C 5a


$a(t_1+t_2)=a$

$t_1+t_2=1$

$PQ=a(t_1-t_2{)}^2$

$=a\left[\right(t_1+t_2{)}^2-4t_1{t}_2]$

$=a[1+4]=5a$ use (1)