Consider the parametric equation

Options

A. It represents a circle of diameter a
B. It represents a circle of radius a
C. It represents a parabola
D. none of the above

Answer

D

Explanation

`x^(2)+y^(2)=[a(1-t^(2))/(1+t^(2))]^(2)+][(2at)/(1+t^(2))]^(2)`
`=a^(2)(1-t^(2))/(1+t^(2))^(2)+(4a^(2)t^(2))/(1+t^(2))`
`=a^(2)(1+t^(4)+2t^(2))/(1t^(2))=a^(2)(1+t^(2))/(1+t^(2))=a^(2)`
Hence the given equation represent a circle of radius (A)
`therefore` option (b) is correct