Question

a  fixed point A(0,4) is there and a moving point B(2t,0) is there its middle point is M and AB perpendicular bisector is MR where R is a point on y axis then how to find the equation of middle point of MR

Answer 1

look at diagram
i have taken R as (0,a) as lies on y axis
slope of AB
$\frac{0-4}{2t-0}= \frac{-2}{t}$
the slope of MR is $\frac{t}{2}$
$\frac{a-2}{-t}= \frac{t}{2} \\ a= \frac{4-t^2}{2}$
so its middle point is
$( \frac{a+t}{2} ,\frac{2+0}{2} )=( \frac{4+2t-t^2}{4} ,1)$