Question

If $y=2x+3$ is a tangent to the parabola , $y^2=24x$ ,then its distance from parallel normal is

• A. $5\sqrt{5}$
• B. $10\sqrt{5}$
• C. $15\sqrt{5}$
• D. none of these

Answer 1

The correct option is C $15\sqrt{5}$

Given,

$y^2=24x$

$4a=24$

$\therefore a=6$

$y=2x+3$

$\therefore m=2$

equation of normal

$y=mx-2am-a{m}^3$

substituting the values of "m" and "a", we get,

$\therefore y=2x-72$

$y=2x-3=\frac{75}{\sqrt{1+2^2}}=\frac{75}{\sqrt{5}}=15\sqrt{5}$