Find all points on the curve x^2y^2+2xy=3 where the slope of the tangent is -1. If there is more than one point, use a comma to separate each pair of coordinates
3 answers
Do you mean the curve x^2 + y^2 + 2xy = 3?
On second thoughts, I don't think you do mean that: if you did, the tangent would be -1 for every point on the curve.
If it IS x²y² + 2xy = 3, then put z=xy for a moment, in which case z²+2z=3, in which case z=1 or z=-3. So xy=1 or xy=-3, i.e. y=1/x or y=-3/x. If you differentiate each with respect to x and solve for dy/dx = -1, you should get the answers you need.
If it IS x²y² + 2xy = 3, then put z=xy for a moment, in which case z²+2z=3, in which case z=1 or z=-3. So xy=1 or xy=-3, i.e. y=1/x or y=-3/x. If you differentiate each with respect to x and solve for dy/dx = -1, you should get the answers you need.
Big juicy pickle