Question

Assertion :The ratio of length of tangent to length of normal is proportional to the ordinate of the point of tangency at the curve $y^2=4ax$ Reason: Length of normal and tangent to a curve $y=f\left(x\right)$ is $\left|y\sqrt{1+m^2}\right|$ and $\left|\frac{y\sqrt{1+m^2}}{m}\right|$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$y^2=4ax$
$\Rightarrow \frac{dy}{dx}=\frac{2a}{y}=m$ (say)
Thus length of Tangent is $=\left|\frac{y}{m}\sqrt{1+m^2}\right|$
And length of Normal is $=|y\sqrt{1+m^2}|$
Hence ratio of length of tangent to the length of normal is $=\frac{1}{m}=\frac{y}{2a}$
Hence both the assertion and reason are correct and the assertion is followed by the reason.