Find the normal to the curve x^2 + y^2 = 2x + 2y that is parallel to the line x+y = 0
Hello, yakkow!
Differentiate implicitly: .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!