See answer: Exercises 51 through 60 are concerned with conics. A conic is a curve in M2

Chapter 1, Problem 60

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Exercises 51 through 60 are concerned with conics. A conic is a curve in M2 that can be described by an equation of the form fix, y) = cj + c2x + c3y + c4x2 + csxy + C6y2 = o, where at least one of the coefficients c, is nonzero. Examples are circles, ellipses, hyperbolas, and parabolas. If k is any nonzero constant, then the equations f(x, y) = 0 and kf(x, y) = 0 describe the same conic. For example, the equation -4 + x2 + y2 = 0 and 12 + 3x2 + 3y2 = 0 both describe the circle of radius 2 centered at the origin. In Exercises 51 through 60, find all the conics through the given points, and draw a rough sketch of your solution curve(s). (0,0), (2,0), (0,2), (2, 2), (1,3), and (4, 1).