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प्रश्न
Find the equation of the tangent and the normal to the following curve at the indicated point y = x2 at (0, 0) ?
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उत्तर
\[y= x^2 \]
\[\text { Differentiating both sides w.r.t.x,} \]
\[\frac{dy}{dx} = 2x\]
\[\text { Given } \left( x_1 , y_1 \right) = \left( 0, 0 \right)\]
\[\text { Slope of tangent,}m= \left( \frac{dy}{dx} \right)_\left( 0, 0 \right) =2\left( 0 \right)=0\]
\[\text { Equation of tangent is },\]
\[y - y_1 = m\left( x - x_1 \right)\]
\[ \Rightarrow y - 0 = 0 \left( x - 0 \right)\]
\[ \Rightarrow y = 0\]
\[\text { Equation of normal is,}\]
\[ \Rightarrow y - y_1 = \frac{- 1}{m} \left( x - x_1 \right)\]
\[ \Rightarrow y - 0 = \frac{- 1}{0} \left( x - 0 \right)\]
\[ \Rightarrow x = 0\]
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