YOU CAN SKIP QUESTION 3, PLEASE JUST SOLVE QUESTION 1, 2, 4 AND PLEASE SHOW WORK ASSOCIATED WITH IT. I WILL PROVIDE FULL POSITIVE FEED BACK AND 5 STAR RATING THANK YOU SO MUCH!!!

Many of the following are modified versions of exercises from Stewart's Multivariable Calculus. Note: while the concept of curvature below will not show up on the exams, it does appear in the labs. The curvature of a space curve with vector function r is given by K(t) = |r'(t) x r" (t) | |r (t) 13 1. Find parametric equations for two circles C1 and C2 in space such that . C1 and C2 have the same radius; . C1 and C2 intersect at the points P(1, 2, -1) and Q(1, 2, 1) and nowhere else. 2. Show that the space curve with parametric equation r(t) = (t - 2t2, 4 - 6t, t2 - 1) lies in a plane, and find an equation of this plane. Hint: try a plane ax + by + cz + d = 0. 3. Do exercises 21-26 of $13.1 of Stewart's Multivariable Calculus. 4. Find a parametric equation which describes the curve defined by intersecting the cylinder x2 + 2? = 625 with the revolutionary paraboloid 4y + (x2 + z2) = 0. Sketch the surfaces and the curve