Find the slope of the tangent to the curve x^2+xy+y^2=4 at the point(2,-2)

Question

please show workings
#thanks

Answer 1

differentiate implicitly,

x^2 + xy + y^2 = 4
2x + x y' + y + 2y y' = 0
y' (x + 2y) = -2x - y
y' = (-2x-y)/(x+2y)
for (2,-2)
y' = (-4 + 2)/(2 -4)
= -2/-2 = 1