Question

The locus of the point $\left(x,y\right)$ whose distance from the line $y=2x+2$ is equal to the distance from $\left(2,0\right)$ , is a parabola with the length of latus rectum same as that of the parabola $y=K{x}^2,$ then the value of $K$ is equal to

• A. $\frac{\sqrt{5}}{12}$
• B. $\frac{\sqrt{5}}{4}$
• C. $\frac{4}{\sqrt{5}}$
• D. $\frac{12}{\sqrt{5}}$

Answer 1

Answer: (A)

Length of $LR=2\left(SM\right)$
$=2$ $\frac{|2\left(2\right)+2-0|}{\sqrt{2^2+1}}=\frac{12}{\sqrt{5}}$
$\Rightarrow \frac{1}{K}=\frac{12}{\sqrt{5}}\Rightarrow K=\frac{\sqrt{5}}{12}$