JEE Main 2020 (Online) 2nd September Morning ShiftQuestion 1
Let $P(h,k)$ be a point on the curve $y=x^2+7x+2$, nearest to the line, $y=3x-3$. Then the equation of the normal to the curve at $P$ is :
Differentiation and its Application
Solution
Concept. The curve does not meet the line, so at the nearest point the tangent is parallel to the line. Formulas used. (1) $x^2+7x+2=3x-3\iff x^2+4x+5=0$, discriminant $<0$ (no intersection)(2) $y'=2x+7$Step 1 - Point. By (2), $2h+7=3$, so $h=-2$ and $k=4-14+2=-8$.Step 2 - Normal. Slope $-\frac13$: $y+8=-\frac13(x+2)$, i.e. $x+3y+26=0$. Answer: (C)