1. Describe an ellipse in two sentences.2. Find the standard form of the equation of the ellipse and give the location of its foci.Standard form of equation of an ellipse with center at the origin, and major and minor axes of lengths 2a and 2b (where a and b are positive, and a2 > b2) is:The location of foci are at (–c, 0) and (c, 0) where c2 = a2 – b2.3. Graph the ellipse.a. b. c. d. [Hint: In order to graph this ellipse, find the center (h, k) by comparing the given equation with the standard form of equation centered at (h, k). Next, find a and b. Find the vertices (h – a, k) and (h + a, k). Find the foci (h + c, k) and (h – c, k).]4. A semielliptic archway has a height of 20 feet and a width of 50 feet, as shown in the figure below. Can a truck 14 feet high and 10 feet wide drive under the archway without going into the other lane?50 ft20 ft5. Find the standard form of the equation of the hyperbola whose graph is given below.6. Find the vertices of the hyperbola.7. What is a parabola? Describe in two sentences.8. The giant Arecibo telescope in Puerto Rico has a parabolic dish with a diameter of 300 meters and a depth of 50 meters. (Source: National Astronomy and Ionosphere Center, Arecibo Observatory.)a. Find an equation in the form that describes a cross section of this dish.b. If the receiver is located at the focus, how far should it be from the vertex?
