Question

Statement-1: The line $x - 2y = 2$ meets the parabola, $y^2 + 2x = 0$ only at the point $(- 2,-2)$.
Statement-1: The line $ y=mx-\frac{1}{2m}\left(m\ne0\right)$ is tangent to the parabola, $y^{2} = - 2x$ at the point $\left(-\frac{1}{2m^{2}}, -\frac{1}{m}\right).$

• A. Statement-1 is true; Statement-2 is false
• B. Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1
• C. Statement-1 is false; Statement-2 is true
• D. Statement-1 a true; Statement-2 is true; Statement-2 is not a correct explanation for statement-1

Answer 1

Answer: (B)

Both statements are true and statement-2 is the correct explanation of statement-1
$\therefore $ The straight line $y=mx+\frac{a}{m}$ is always a tangent to the parabola $y^{2}=4ax$ for any value of $m$.
The co-ordinates of point of contact $\left(\frac{a}{m^{2}}, \frac{2a}{m}\right)$