find the points on the curve [(x^2 )+ (y^2) = 18] at which the tangents are parallel to the line x+y = 3

Answer 1

the line has slope -1

x^2+y^2=18
dy/dx = -x/y

so, we need x = y

x^2+x^2 = 18
x = ±3, so the points are

(-3,-3) and (3,3)

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plot x^2+y^2=18, x+y = -6, x+y=6, x=3, y=3