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A point P(x , y) moves in the xy-plane s...

A point `P(x , y)` moves in the xy-plane such that `x=acos^2theta` and `y=2asintheta,` where `theta` is a parameter. The locus of the point `P` is a/an

A

circle

B

ellipse

C

unbounded parabola

D

part of the parabola

Text Solution

Verified by Experts

The correct Answer is:
D
(4) Eliminating `theta` from the given equations, we get
`y^(2)=-4a(x-a)`
which is a parabola but
`0lecos^(2)thetale1`
`or" "0lexlea`
`and" "-1lesinthetale1`
`or" "-2aleyle2a`
Hence, the locus of point P is not whole parabola, but it is a part of the parabola.
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