Question

Assertion :The equation $y=mx-a{m}^2$ is tangent to the parabola $x^2=4ay\forall m\in R$. Reason: A straight line $y=mx+c$ which intersect the parabola $x^2=4ay$ at one point is tangent line.

• 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

$\because x^2=4a(mx+c)$ $\Rightarrow x^2-4amx-4ac=0....\left(1\right)$

The line $y=mx+c$ wil! be tangent to parabola if both roots
of $\left(1\right)$ be equal $\therefore D=0$ $\Rightarrow 16a^2{m}^2+4\left(4ac\right)=0\Rightarrow c=-a{m}^2\therefore$ Equation of tangent
be $y=mx-a{m}^2$
So Assertion & Reason both are true & Reason (R) is correct
explanation of Assertion (A),