Let P(h, k) be a point on the curve y = x2 + 7x + 2, nearest to the line, y = 3x -- 3.

Question

Let P(h, k) be a point on the curve

y = x2
 + 7x + 2, nearest to the line, y = 3x -- 3.

Then the equation of the normal to the curve at
P is :

Accepted Answer

Let L be the common normal to parabola

y = x2
 + 7x + 2 and line y = 3x -- 3

Slope of tangent of y = x2
 + 7x + 2 at P

$${{{\left. {{{dy} \over {dx}}} \right|}_{P}}}$$ = 3

$$ \Rightarrow $$ 2x + 7 = 3

$$ \Rightarrow $$ x = -2

$$ \therefore $$ y = -8

So P(--2, --8)

Normal at P : x + 3y + C = 0

$$ \Rightarrow $$ -2 + 3(-8) + C = 0

$$ \Rightarrow $$ C = 26

$$ \therefore $$ Normal : x + 3y + 26 = 0

Solutions · 1