Question

If one end of focal chord $PQ$ of the parabola $y^2=8x$ is at $P(\frac{1}{2},-2),$ then the equation of tangent to it at $Q$ is

• A. $x+2y+8=0$
• B. $2x-y-24=0$
• C. $x-2y+8=0$
• D. $2x+y-24=0$

Answer 1

The correct option is C $x-2y+8=0$

$PQ$ is the focal chord of the parabola $y^2=8x$
$P\left(t_1\right)=(2t_1^2,4t_1),Q\left(t_2\right)=(2t_2^2,4t_2)$
$\Rightarrow t_1{t}_2=-1$

$(\frac{1}{2},-2)=(2t_1^2,4t_1)\Rightarrow t_1=-\frac{1}{2}\Rightarrow t_2=2$

So, $Q=(8,8)$
The equation of the tangent at $Q$ is
$T=0\Rightarrow 8y=4(x+8)\therefore x-2y+8=0$