Find the normal to the curve x^2 + y^2 = 2x + 2y that is parallel to the line x+y = 0

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- June 13th 2006, 03:54 PMyakkowStuck... beginner
Find the normal to the curve x^2 + y^2 = 2x + 2y that is parallel to the line x+y = 0

- June 13th 2006, 04:26 PMSoroban
Hello, yakkow!

Quote:

Find the normal to the curve that is parallel to the line

Factor: . . . . slope of the*tangent*

The slope of the*normal*is: .

The line has slope

So we have: .

Substitute into the original equation:

. . .

The corresponding y-values are:

We seem to have**two**normals: one at (2,0), another at (0,2)

At (2,0) with slope -1, the equation of the normal is:

. . .

At (0,2) with slope -1, the equation of the normal is:

. . .

*Ha!*. . . It's the same line!