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 $y=Kx^{2},$ 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 $LR=2\left(S M\right)$
$=2$ $\frac{\left|2 \left(2\right) + 2 - 0\right|}{\sqrt{2^{2} + 1}}=\frac{12}{\sqrt{5}}$
$\Rightarrow \frac{1}{K}=\frac{12}{\sqrt{5}}\Rightarrow K=\frac{\sqrt{5}}{12}$