Given the characteristics of each conic, solve for the equation in standard form then graph. Show complete solution (3 points) then graph and label properly all important characteristics of the conic. (2 points) 1. Circle tangent to both axes at (3, 0) and (U, 3). 2. Parabola with x + 1 = 0 as the directrix, y = 1 as the axis, and the length of the Iatus rectum is 4. 3. Ellipse with foci at (2, 3) and (2, 1), and an endpoint of the minor axis at (4, 1). 4. Hyperbola with the same vertices as the yertices of the ellipse 9x2 + 43:2 = 36 and with the asymptotes y = J_r 3 x. Challenge yoursetf with these questions. (5 points each) 5. Find the equation of the circle, if the center of the circle of radius 3 lies on the line x + 2y = 4 and it is tangent to the y axis. 6. Show that the product of the distances of any point of a hyperbola from its asymptotes is constant