show that the curves 3x^2+2x-3y^2=1 and 6xy+2y=0 are orthogonal (i.e. there slopes everywhere are perpendicular)
thank you, your help is very appreciated!
If you take the derivatives of both curves wrt x then the derivative of the first curve is (3x+1)/(3y) and the derivative of the second curve wrt x is
(-3y)/(3x+1). So the slopes are opposite reciprocals. This means they are perpendicular. Hope this helps, someone else will hopefully explain it better.