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$The normal to a curve at p(x,y) meets the x-axis at G. If the distance of G from the origin is twice the abscisa of P, then the curve is a$

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Correct option is C

Equation of the normal Y−y=−dxdy(X−x), meets x axis ⇒Y=0-y=−dxdy(X−x)ydydx=X-x ⇒X=x+ydydx and Y=0then Gx+ydydx,0⇒OG=2x⇒x+ydydx=2x⇒∫ydy=∫xdx⇒y22=x22+c⇒x2−y2=c

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