Mathematics · 2013
JEE Main · 22 April 2013, Shift 1 · Q73
Statement 1: The line x-2 y=2 meets the parabola, y^2+2 x=0 only at the point (-2,-2): Statement 2: The line y= m x-1/(2 m)( m ≠ 0) is tangent to the…
Statement $\displaystyle 1$ : The line $\displaystyle x-2 y=2$ meets the parabola, $\displaystyle y^2+2 x=0$ only at the point
$$(-2,-2):
$$Statement $\displaystyle 2$ : The line $\displaystyle y=\mathrm{m} x-\frac{1}{2 \mathrm{~m}}(\mathrm{~m} \neq 0)$ is tangent to the parabola, $\displaystyle y^2=-2 x$ at the point $\displaystyle \left(-\frac{1}{2 \mathrm{~m}^2},-\frac{1}{\mathrm{~m}}\right)$.
Official answer
(2)
Statement $\displaystyle 1$ is true ; Statement $\displaystyle 2$ is true ; Statement $\displaystyle 2$ is a correct explanation for Statement 1.
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JEE Main 2013 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.