jee-main 2017 Q81

jee-main · India · 02apr Tangents, normals and gradients Normal or perpendicular line problems

The normal to the curve $y(x - 2)(x - 3) = x + 6$ at the point where the curve intersects the $y$-axis passes through the point:
(1) $\left(-\dfrac{1}{2}, -\dfrac{1}{2}\right)$
(2) $\left(\dfrac{1}{2}, \dfrac{1}{2}\right)$
(3) $\left(\dfrac{1}{2}, -\dfrac{1}{3}\right)$
(4) $\left(\dfrac{1}{2}, \dfrac{1}{3}\right)$

The normal to the curve $y(x - 2)(x - 3) = x + 6$ at the point where the curve intersects the $y$-axis passes through the point:\\
(1) $\left(-\dfrac{1}{2}, -\dfrac{1}{2}\right)$\\
(2) $\left(\dfrac{1}{2}, \dfrac{1}{2}\right)$\\
(3) $\left(\dfrac{1}{2}, -\dfrac{1}{3}\right)$\\
(4) $\left(\dfrac{1}{2}, \dfrac{1}{3}\right)$

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