Question

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

• A. $2$
• B. $4$
• C. $6$
• D. none of these

Answer 1

The correct option is B $4$

Parabola: $y^2=4x............\left(1\right)$ $(a=1)$

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

So, line passing through $(1,2)$ and $(1,0)$,

$=>(y-0)=\frac{2-0}{1-1}(x-1)$

$=>x=1.............\left(2\right)$

Line $\left(2\right)$ is perpendicular to axis of parabola and passes through focus$=>$ line $\left(2\right)$ is $LR$ and

length of $LR=4\left(a\right)=4\left(1\right)$

$=4.$