Find the point P on the curve y2 = 4ax which is nearest to the point

Question

(11a, 0).

Answer 1

the distance z from (x,y) to (11a,0) is

z = √((x-11a)^2 + y^2)
= √((x-11a)^2 + 4ax)
= √(x^2-18ax+121a^2)

dz/dx = (x-9a)/√(x^2-18ax+121a^2)
dz/dx=0 when x = 9a

So, P is (9a,6a)