Question

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

• A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
• B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
• C. Statement-1 is true, statement-2 is false.
• D. Statement-1 is false, statement-2 is tru

Answer 1

Answer: (A)

The line of slope $=m$ given by $y=m x+c$ is tangent to parabola $y^2=4 a x$, if $c=\frac{a}{m}$ and the point of contact is $\left(\frac{ a }{ m ^2}, \frac{2 a }{ m }\right)$.
Here, $m =\frac{1}{2}, c =-1$ and $a =\frac{-1}{2}$