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A curve C with negative slope through th...

A curve C with negative slope through the point (0, 1) lies in the first quadrant. The tangent at any point P on it meets the x-axis at Q such that PQ = 1. Then the curve in parametric for is

A

Circles

B

Parabolas

C

Ellipses

D

Hyperbolas

Text Solution

Verified by Experts

The correct Answer is:
A
Replacing `(dy)/(dx) by (-dy)/(dx)` in (1), we get
`(-dx)/(dy) = (-y)/sqrt(1-y^(2))`
`rArr -2intdx= int(-2ydy)/sqrt(1-y^(2))`
`rArr -2intdx = int(-2ydy)/sqrt(1-y^(2))`
`rArr -2x-2c=2sqrt(1-y^(2))`
`rArr (x+c)^(2)+y^(2)=1`, which are required orthogonal trajectories.
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