Find the point on the parabola x+y^2=0 that is closest to the point (0,-3).

Answer 1

the distance d is found using

d^2 = x^2 + (y+3)^2

Since x = -y^2, that means

d^2 = y^4 + (y+3)^2

Now all you do is find dd/dy = 0 and that is where the distance is minimum. Then evaluate x = -y^2 and you have your point.