The curve for which the normal at any point P(x,y) and the line joining origin to the point P form an isosceles triangle with x−axis as base is
A
A rectangular hyperbola
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B
An ellipse
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C
A parabola
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D
A circle
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Solution
The correct option is D A circle It is given that the triangle OPG is an isosceles triangle. Therefore, OM=MG= sub-normal ⇒x=∣∣∣ydydx∣∣∣⇒xdx=±ydy
On intergating both sides, we get x2−y2=C, or x2+y2=c which is a rectangular hyperbola or a circle.