Hello!

Need to find the shortest distance between two curves by the method of gradient descent:

x^2+y^2-2*x+4*y+3 = 0 and x = (cosϕ)^3 − 1, y = 2 + (sinϕ)^3

The crux of the matter is that I can't be a function of the distance between points on these lines to minimize. Tell me how to do it? Thanks in advance

Need to find the shortest distance between two curves by the method of gradient descent:

x^2+y^2-2*x+4*y+3 = 0 and x = (cosϕ)^3 − 1, y = 2 + (sinϕ)^3

The crux of the matter is that I can't be a function of the distance between points on these lines to minimize. Tell me how to do it? Thanks in advance

asked March 19th 20 at 09:16

1 answer

answered on March 19th 20 at 09:18

There is a formula for the distance between two points:

That's it, substitute x and y from the first and second equations, and in the first have to Express x through y.

Get a function of the distance between two arbitrary points of the curves:

p.s.

If we are talking about real numbers.

`sqrt((x2-x1)^2+(y2-y1)^2)`

That's it, substitute x and y from the first and second equations, and in the first have to Express x through y.

Get a function of the distance between two arbitrary points of the curves:

`d = f(x; f) >= 0`

p.s.

If we are talking about real numbers.

I know this equation, I have a problem just the same is to Express x and y from the first equation of the curve - Wade_Barrows76 commented on March 19th 20 at 09:21

@Wade_Barrows76, y= -2 +- sqrt(1 + 2 x - x^2) - elvie_Tromp63 commented on March 19th 20 at 09:24

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