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 11:2 + :92 = 1 represents the circle 0 of radius 1 centered at the origin of the real plane R2. Over the real numbers again, the equation my = 1 represents an hyperbola (also written as y = l), I: which we denote by H. (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: \"loopiness..\