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Q.

A normal at p(x,y) on a curve meets the x -axis at Q and N is the foot of the  ordinate at P . If NQ=x1+y21+x2, then the equation of the curve given that it passes through the point (3,1) is

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a

x2-y2=8

b

x2+2y2=11

c

x2-5y2=4

d

x2+5y2=4

answer is C.

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Detailed Solution

Equation of the normal Y−y=−dxdy(χ−x) NQ=ydydx=x(1+y2)1+x2⇒∫xdx1+x2=∫ydy1+y2⇒log⁡1+x2=log⁡1+y2+log⁡c⇒1+y2=1+x2c pass (3,1)⇒c=5⇒5+5y2=1+x2
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A normal at p(x,y) on a curve meets the x -axis at Q and N is the foot of the  ordinate at P . If NQ=x1+y21+x2, then the equation of the curve given that it passes through the point (3,1) is