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 circle (b) aellipse unbounded parabola (d) part of the parabola

Options

A. circle
B. ellipse
C. unbounded parabola
D. part of the parabola

Answer

D

Explanation

(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.