A cable has to connect between a point 3 distance units south of the origin i.e. (0, −3) and the parabola y^2 = −x. Find the point on the parabola if the cable length is to be minimised.

Question

A cable has to connect between a point 3 distance units south of the origin i.e. (0, −3) and  the parabola y^2 = −x. Find the point on the parabola if the cable length is to be minimised.

amistre64 · Answer

d^2 = (x-x1)^2 + (y-y1)^2

might be useful in this

anonymous · Answer

What do I do with that?

amistre64 · Answer

d' = 2x'(x-x1) + 2y'(y-y1)

0 = x'(x-x1) + y'(y-y1)

let x1, y1 be the point;  and let x = -y^2,  and y = y  be the second point
                                                      x' = -2y            y' = 1

0 = -2y(-y^2-0) + (y+3)

0 = 2y^3+y+3

solve for y

amistre64 · Answer

might do better with a different choice of the issues

amistre64 · Answer

the wolf makes it simple.

another route is to simply find when the slope between (0,-3) and (-y^2,y)  is perp to the tangent of the parabola

amistre64 · Answer

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