Question

Could someone help me to find a tool or a hint to find the parametric form of this equation xy-y^2=1? (ref. Pset 4 Problem 2 ). Does the "answer" lie in single variable calculus? Please don't tell me the answer, I just want to know where to look and what tools I should use. Thanks

Answer 1

My answer is related to Multivariable calculus 2010

Answer 2

I need help please

Answer 3

First, we parameterize\[z=2+(x-y)^2\]Let t=x-y. Now we have z as a function of t:\[z=2+t^2\]Insert this value of t into your second equation\[z=x^2-y^2=(x-y)(x+y)\]We get:\[2+t^2=t(t+2y)\]Now solve for y in terms of t. Once you have y in terms of t, then solve for x in terms of t using t=x-y. You will then have x,y and z in terms of the parameter t; thus your parametric equations of the surface of intersection.