Question

The point on the parabola $y=x^2+7x+2$ which is closest to the line $y=3x-3$ is

• A. $(2,20)$
• B. $(1,10)$
• C. $(-3,-28)$
• D. $(-2,-8)$

Answer 1

The correct option is D $(-2,-8)$

Parabola is $y=x^2+7x+2$
Differentiating the given curve w.r.t to $x$, we get
$\frac{dy}{dx}=2x+7$, which geometrically represents slope of the tangent to the curve $y=f\left(x\right)$
$\because$ for shortest distance ,slope of tangent and slope of the line should be same.
The slope of line $y=3x-3$ is $3$
$\therefore 2x+7=3\Rightarrow x=-2$
Here put $x=-2$ in the given curve, we get $y=-8$
$\therefore$ the point is $(-2,-8)$