what is the shortest distance between a parabola and the circle? what is the shortest distance between the parabola and the circle?
the equation of parabola is $$y^2=4ax$$
and the equation of circle is $$x^2+y^2-24y+81=0$$
if you can show graphically it will be more helpful!! thanks

HINT...find the general equation of the normal to the parabola at the point $P(at^2, 2at)$ and find the value of $t$ for which this normal passes through the centre of the circle. Then you can find the closest point on the parabola (with this value of $t$), and the rest is just considering distances and the radius of the circle.
