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  • Let P(h,k) be a point on the curve  nearest to the line, <img alt="y= 3x-3," src="https://entrancecorner.codecogs.com/gif.late

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:
Option: 1 x+3y+26=0
Option: 2 x+3y-26=0
Option: 3 x-3y-11=0  
Option: 4 x-3y+22=0

Answers (1)

best_answer

Let L be the common normal to the parabola

y=x^{2}+7 x+2 \text { and line } y=3 x-3

\begin{aligned} &\Rightarrow \text { slope of tangent of } y=x^{2}+7 x+2 \text { at } P=3\\ &\left.\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}\right]_{\text {for } \mathrm{P}}=3\\ &\Rightarrow 2 x+7=3 \Rightarrow x=-2 \Rightarrow y=-8\\ &\text { So } \mathrm{P}(-2,-8) \end{aligned}

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

⇒C = 26 (P satifies the line)

Normal : x + 3y + 26 = 0

Posted by

himanshu.meshram

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