If tangent at a point P(x,y) of a curve is perpendicular to line that joins origin with point P , th

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10-1.Circle and System of Circles

easy

If the tangent at a point $P(x,y)$ of a curve is perpendicular to the line that joins origin with the point $P$, then the curve is

A

Circle

B

Parabola

C

Ellipse

D

Straight line

Solution

(a) The tangent drawn at point $P(x,\;y)$ on the circle ${x^2} + {y^2} = {a^2}$ is perpendicular to the line that joins the origin with point $P$.

So required curve will be circle.

Standard 11

Mathematics

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