Question

The point $(1,2)$ is one extremity of focal chord of the parabola $y^2=4x$. The length of this focal chord is

• A. $1$
• B. $2$
• C. $4$
• D. $8$

Answer 1

The correct option is C $4$

Parabola:
$y^2=4x\Rightarrow a=1$

The point $(1,2)$ is end of focal chord, As focal chord passes through focus, the focal chord must pass through $(a,0)$ i.e. $(1,0)$

So, line passing through $(1,2)$ and $(1,0)$ will be $x=1$

Since $x=1$ is perpendicular to axis of parabola and passes through focus

$\Rightarrow x=1$ is latus rectum and length of latus rectum $=4\left(a\right)=4$