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  • Find the equation of the normal to the parabola x2 = 4y at the point (2, 1)Option: 1 <img alt="x-y+3=0" src="https://learn.careers360.com/

Find the equation of the normal to the parabola x2 = 4y at the point (2, 1)

Option: 1

x-y+3=0


Option: 2

x-y=3


Option: 3

x+y=3


Option: 4

x+y+3=0


Answers (1)

best_answer

As we have learnt
\begin{array}{c||c c} \\ \mathbf { Equation \;of \;Parabola } & {\mathbf { \;Normal\; at\; } P\left(x_{1}, y_{1}\right)} \\ \\ \hline \hline\\y^{2}=4ax & y-y_1=-\frac{y_1}{2a}(x-x_1) & {} \\\\ {y^{2}=-4 a x} & {y-y_1=\frac{y_1}{2a}(x-x_1)} & {} \\\\ {x^{2}=4 a y} & {y-y_1=-\frac{2a}{x _1}(x-x_1)} & {} \\\\ {x^{2}=-4 a y} & {y-y_1=\frac{2a}{x_1}(x-x_1)} & {} \\ \end{array}

 

The equation of the normal to such a parabola is

\begin{aligned} & y-y_{1}=-\frac{2 a}{x_{1}}\left(x-x_{1}\right), \text { where } a=1 \\ \Rightarrow \quad & y-1=-\frac{2}{2}(x-2)=-x+2 \\ \Rightarrow \quad & x+y=3 \end{aligned}

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