Find the equation of the circle, one of whose diameters is the latus rectum y2=4ax. Show that this circle goes through the common point of the axis and the directrix of the parabola.
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Solution
Latus rectum and points of y2=4ax
arc(a,2a) & (a−2a)
centre =(a,0)
Radius =2a+2a2=2a
Circle (x−a)2+y2=4a2
It also passes through (−a,0)
(−a−a)2+02=4a2
4a2=4a2
(−a,0) is intersection point of direction & axis of parabola