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The curve in the first quadrant for whic...

The curve in the first quadrant for which the normal at any point `(x , y)` and the line joining the origin to that point form an isosceles triangle with the x-axis as base is (a) an ellipse (b) a rectangular hyperbola (c) a circle (d) None of these

A

an ellipse

B

a rectangular hyperbola

C

a circle

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
It is given that triangle OPG is an isosceles triangle.

Therefore, OM=MG= sub-normal
or `x=y(dy)/(dx)` or `xdx=ydx`
On integration, we get `x^(2)-y^(2)=C`, which is a rectangular hyperbola.
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