VJC P1 Q6

A curve has equation and a line has equation as shown above.

is a fixed point on C and A is an arbitrary point on . State the geometrical relationship between the line segment AB and is the distance from B to A is the least.

Taking the coordinates of A as , find an equation relating and for which AB is the least.

Deduce that when AB is the least, where is a constant to be found. Hence or otherwise, find the coordinates of the point on C that is nearest on .