Question

Find the equation of the tangent and the normal to the following curve at the indicated point  y = x² at (0, 0) ?

Answer 1

\[y= x^2 \]

\[\text { Differentiating both sides w.r.t.x,} \]

\[\frac{dy}{dx} = 2x\]

\[\text { Given } \left( x_1 , y_1 \right) = \left( 0, 0 \right)\]

\[\text { Slope of tangent,}m= \left( \frac{dy}{dx} \right)_\left( 0, 0 \right) =2\left( 0 \right)=0\]

\[\text { Equation of tangent is },\]

\[y - y_1 = m\left( x - x_1 \right)\]

\[ \Rightarrow y - 0 = 0 \left( x - 0 \right)\]

\[ \Rightarrow y = 0\]

\[\text { Equation of normal is,}\]

\[ \Rightarrow y - y_1 = \frac{- 1}{m} \left( x - x_1 \right)\]

\[ \Rightarrow y - 0 = \frac{- 1}{0} \left( x - 0 \right)\]

\[ \Rightarrow x = 0\]