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  • If the line is a tangent to <img alt="\mathrm{y^{2}=4 m x}" src="https://ent

If the line \mathrm{y=m x+c} is a tangent to \mathrm{y^{2}=4 m x}, then distance of this tangent from the parallel normal is

Option: 1

\mathrm{\sqrt{1+m^{2}}}


Option: 2

\mathrm{\sqrt{2+m^{2}}}


Option: 3

\mathrm{\left(1+m^{2}\right)^{3 / 2}}


Option: 4

\mathrm{\left(2+m^{2}\right)^{3 / 2}}


Answers (1)

best_answer

Equation of parallel normal is
\mathrm{y=m x-2 m^{2}-m^{4}}
\mathrm{\Rightarrow \quad \text { Required distance }= \frac{\left|c+2 m^{2}+m^{4}\right|}{\sqrt{1+m^{2}}}}

Here, \mathrm{c=1}
Thus required distance \mathrm{=\left(1+\mathrm{m}^{2}\right)^{3 / 2}}

Posted by

Suraj Bhandari

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