I want to find the coordinates where the tangent to the curve is parallel to the x and y axis.
The curve is $$2x^2 +xy - y^2 +18 = 0 $$
$$ Dy/dx = (-4x-y)/(x-2y) $$
Am I correct in saying that to work out the tangent parallel to x axis, I would say that -4x-y=0 as the tangent would be horizontal and so the change in y has to be zero as therefore $$0=0/(x-2y). $$
Subsequently, to work out the tangent to the y axis, is it x-2y=0 as the change in x would be 0 as the tangent would be vertical and so $$0=-4x-y$$