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 .
If the distance is the least, then AB is perpendicular to .
since and AB is perpendicular to .
Differentiating with respect to b,