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Question

The equation of the tangent at (x1,y1) to a curve y2=4ax at a point (x1,y1) is given by yy1=2a(x+x1)


A

True

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B

False

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Solution

The correct option is A

True


The situation can be repersented as below

We know that equation of tangent at (x1,y1) to a curve y=f(x) is given by

yy1=[dydx](x1,y1)(xx1)

curve is

y2=4ax

2y.dydx=4a

dydx=2ay

[dydx](x1,y1)=2ay1

So the equation of tangent to y2=4ax at (x1,y1) is given by

yy1=2ay1(xx1)

yy1y21=2ax2ax1

substracting 2ax1 from both sides

yy1y212ax1=2ax4ax1

yy12ax1=2ax(since y21=4ax1)

yy1=2a(x+x1)

The given statement is true


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