3. In analytic geometry we represent geometrical shapes (\"regular\" shapes, not fractals) by solutions of equations. Let us consider two basic examples of so called conics. Over the real numbers, the equation 2:2 + 312 = 1 represents the circle C of radius 1 centered at the origin of the real plane R2. Over the real numbers again, the equation my 2 1 represents an hyperbola (also written as y = l), which we denote by H. a: (a) What does it means mathematically for an equation representing an geometric gure? (b) How do you check if a given point (a, b) belongs to the circle 0 dened above, or to the hyperbola H? (c) Sketch C' and H, and nd two interesting and noticeable key differences (hint: \"100piness..\