Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. a. Focus: (0, -1) Find the standard form of the equation of the ellipse with the given characteristics. a. Center: (4,-4); vertex:(4,-2); minor axis length 2 Find the standard form of the equation of the ellipse with the given characteristics. a. Vertices: (6, 0), (6, 14); endpoints of the minor axis: (1, 7), (11, 7) Find an equation of the ellipse with the given characteristics. a. vertices: (0, 12); eccentricity: Ya . A mason is building a semielliptical fireplace arch that has a height of 2 feet at the center and a width of 10 feet along the base (see figure). The mason draws the semiellipse on the wall using thumbtacks as the foci. a. Find the positions of the thumbtacks. i. Smaller x-value ii. Larger x-value b. Find the length of the string in feet . The first artificial satellite to orbit Earth was Sputnik I (launched by the former Soviet Union in 1957). Its highest point above Earth's surface was 939 kilometers, and its lowest point was 215 kilometers (see figure). The center of Earth was at one focus of the elliptical orbit. a. Find the eccentricity of the orbit. (Assume the radius of Earth is 6378 kilometers. Round your answer to three decimal places.) Find the standard form of the equation of the hyperbola with the given characteristics. a. Vertices: (2, 0); foci: (9, 0) Find the standard form of the equation of the hyperbola with the given characteristics. a. Vertices:(=3, 2), (3, 2); passes through the point (5, 4) Find the standard form of the equation of the hyperbola with the given characteristics. a. Vertices:(2, =2), (2, 6); passes through the point (6, 10) . Find the standard form of the equation of the hyperbola with the given characteristics. a. Vertices: (0, 8); asymptotes: y = +8x . Find the standard form of the equation of the hyperbola with the given characteristics. a. Vertices: (5, -3), (5, =7); b. Asymptotes: y = x 10, y = x . Find the standard form of the equation of the hyperbola with the given characteristics. a. Vertices: (-8, 3), (0, 3); asymptotes: y=x+ 7, y=-x-1 . Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. a. Focus: (0, -1) . Find the standard form of the equation of the parabola with the given characteristics. a. Vertex (2,9); focus (2,7) . Find the standard form of the equation of the ellipse with the given characteristics. a. Center: (5, 6); vertex: (=2, 6); minor axis of length 6
