Question

The coordinates of the point on the parabola $y=x^2+7x+2,$ which is nearest to the straight line y = 3x - 3 are

• A. (-2, -8)
• B. (1, 10)
• C. (2, 20)
• D. (-1, -4)

Answer 1

The correct option is A (-2, -8)

Any point on the parabola is $x,x^2+7x+2,$
Its distance from the line y = 3x - 3 is given by
\(P=$$\left|\begin{array}{c}\frac{3x-(x^2+7x+2)-3}{\sqrt{9+1}}\end{array}\right|$$=\)
$\left|\begin{array}{c}\frac{x^2+4x+5)}{\sqrt{10}}\end{array}\right|=$
$\left|\begin{array}{c}\frac{x^2+4x+5)}{\sqrt{10}}\end{array}\right|$$(as{x}^2+4x+5$ > $0\forall xϵR)$
$\frac{dp}{dx}=0\Rightarrow x=-2$ the required point = (-2, -8)