Calculus 2

Consider the general quadratic equation '+ xy ty- 1-0. Because of the presence of the xy term, we showed in class that the graph of this equation is a conic section rotated by the angle 0 where cot (20) = A - C B Through what angle (in radians, in terms of pi) has this conic been rotated? |47 We also showed in class that we can represent this equation in a rotated uv coordinate system using the equations - u cos(0) - usin(0) and y = usin(0) + vcos(0)........:2::1::: Use your angle @ to write x and y in terms of u and v: Now, substitute these expressions into the original equation to produce a new equation in u and v: Finally, identify the conic: Hyperbola O Parabola O Ellipse