Question

$A=(\sqrt{1-t^2}+t,0)$ and $B=(\sqrt{1-t^2}-t,2t)$ are two variable points where $t$ is a parameter, the locus of the middle point of $AB$ is

• A. a straight line
• B. a pair of straight line
• C. circle
• D. none of these

Answer 1

Answer: (C)

circle

$A=(\sqrt{1-t^2}+t,0)$

$B=(\sqrt{1-t^2}-t,2t$

$M\left(AB\right)=(\sqrt{1-t^2},t)$

$x=\sqrt{1-t^2}$

$y=t$

$x^2=1-y^2$

$x^2+y^2=1$