MHB Finding the point on a parabola closest to a given point

[leprofece]

Find the curve coordinates nearest to P
a)x² = y P(3,0)

ok to the boox exercise model I must do so

(x-3)²+ (y)² = D

then x²-6x +9+y² = D

introducing y into x
y-6sqrt(y) +9 + (y)² = D

derivating
1-3/(sqrt(y) +0+2y

mcm = sqrt(y) -3 +2y = 0
solving
sqrt(y) = -2y+3
Squaring
y = 4y²-12y +9
4y²-13y +9 = 0
x = 1
y = 1

 

[I like Serena]

Find the curve coordinates nearest to P
a)x² = y P(3,0)

ok to the boox exercise model I must do so

(x-3)²+ (y)² = D

then x²-6x +9+y² = D

introducing y into x
y-6sqrt(y) +9 + (y)² = D

derivating
1-3/(sqrt(y) +0+2y

mcm = sqrt(y) -3 +2y = 0
solving
sqrt(y) = -2y+3
Squaring
y = 4y²-12y +9
4y²-13y +9 = 0
x = 1
y = 1

Looks like you already figured this one out. :)