Sullivan, 8th ed. MAC1140, MAC114711.3: The EllipseEquations, given center (h, k), a = distance from center to vertex, b =distance from center to point on minor axis, c = distance from center toeither foci, c 2 = a 2 – b 2, a > b > 0, and major axis equal or parallel to: [1] x-axis   x h y ka b2 22 21  [2] y-axis:   x h y kb a2 22 21  (Note: If a = b, then F1 = F2 and we have a circle.) Find the vertices and foci of each ellipse. Graph each equation.1.x y2 219 4 2. 4y2 + 16x2 = 32 Write an equation for each ellipse:3. Ctr: (0, -3) 4. Ctr: (-2, 2)Sullivan, 8th ed. MAC1140, MAC1147Find the center, vertices, and foci of each ellipse; graph it. (hint: define a and b)5. 9(x - 3)2 + (y + 2)2 = 18 6. 5x2 + 10y2 + 20x – 20y - 10 = 0 7. The arch of a bridge is a semiellipse with a horizontal major axis. The span is 50feet, and the top is 20 feet above the major axis. The roadway is horizontal and 4feet above the top of the arch. Find the vertical distance from the roadway to thearch 15 feet from the center.8. The perihelion (closest point to the sun) of Pluto is 4551 million miles, and the distance of the sun,which is at the focus, from the center of its elliptical orbit is 897.5 million miles. Find the aphelion(farthest distance from the sun) of Pluto. What is the mean distance of Pluto from the Sun? Write anequation for the orbit of Pluto about the Sun.9. An arch for a bridge is a semiellipse with a span of 70 feet. The height of the arch20 feet from the center is 14 feet. What is the height at the center? Let center ofarch =(0,0), a = 35, b = hSullivan, 8th ed. MAC1140, MAC1147Try These38. Graph the equation: x2 + 9y2 + 6x – 18y + 9 = 0a =, b = ; Major axis: Center: Vertices: Foci: 56. The arch of a bridge is a semiellipse with a horizontal major axis. The span is30 feet, and the top of the arch is10 feet above the major axis. The roadway ishorizontal and is 2 feet above the top of the arch. Find the vertical distance fromthe roadway to the arch at 5-food intervals along the roadway. 64. The mean distance of Mars from the Sun is 142 million miles. If perihelion ofMars is 128.5 million miles, what is aphelion? Write an equation for the orbit ofMars about the