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Question

Find the equation of the tangent and the normal to the following curve at the indicated point.
y2=4ax at (x1,y1).

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Solution

y2=4ax
Differentiating both sides w.r.t. x,
2ydydx=4a

dydx=2ay

Slope of tangent at (x1,y1)=(dydx)(x1,y2)=2ay1=m
Equation of tangent is,
yy1=m(xx1)
yy1=2a(xx1)y1
yy1y21=2ax2ax1
yy14ax1=2ax2ax1
yy1=2ax+2ax1
yy1=2a(x+x1)
Equation of normal is,
yy1=1Slopeoftangent(xx1)

yy1=1m(xx1)

yy1=y12a(xx1)
Equation of tangent is yy1=2a(x+x1)
Equation of normal is yy1=y12a(xx1)

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