8.02 1. find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by sixty four = 1. a) center: (0, 0); vertices: (-10, 0), (10, 0); foci: (-8, 0), (8, 0) b) center: (0, 0); vertices: (0, -10), (0, 10); foci: (0, -8), (0, 8) c) center: (0, 0); vertices: (-10, 0), (10, 0); foci: (-6, 0), (6, 0) d) center: (0, 0); vertices: (0, -10), (0, 10); foci: (0, -6), (0, 6) 2. find the center, vertices, and foci of the ellipse with equation 2x2 + 6y2 = 12. a) center: (0, 0); vertices: point negative square root of six comma zero and point square root of six comma zero ; foci: (-2, 0), (2, 0) b) center: (0, 0); vertices: (0, -6), (0, 6); foci: ordered pair zero comma negative four square root two and ordered pair zero comma four square root two ; c) center: (0, 0); vertices: point zero comma negative square root of six and point zero comma square root of six ; foci: (0, -2), (0, 2) d) center: (0, 0); vertices: (-6, 0), (6, 0); foci: ordered pair negative four square root two comma zero and ordered pair four square root two comma zero 3. graph the ellipse with equation x squared divided by twenty five plus y squared divided by four = 1. a) a vertical ellipse is shown on the coordinate plane centered at, five, two, with vertices at, five, seven, and five, negative three and minor axis endpoints at three, two, and seven, two. b) a horizontal ellipse is shown on the coordinate plane centered at five, two, with vertices at zero, two, and ten, two and minor axis endpoints at five, four and five, zero. c) a vertical ellipse is shown on the coordinate plane centered at the origin with vertices at zero, five and zero, negative five and minor axis endpoints at, negative two, zero and two, zero. d) a horizontal ellipse is shown on the coordinate plane centered at the origin with vertices at, negative five, zero and, five, zero and minor axis endpoints at, zero, two and zero, negative two. 4. find an equation in standard form for the ellipse with the vertical major axis of length 6 and minor axis of length 4. a) x squared divided by two plus y squared divided by three = 1 b) x squared divided by nine plus y squared divided by four = 1 c) x squared divided by three plus y squared divided by two = 1 d) x squared divided by four plus y squared divided by nine = 1 5. an elliptical riding path is to be built on a rectangular piece of property, as shown below. a vertical ellipse is shown centered on the coordinate plane, surrounded by a rectangle of equal length and width. the rectangular piece of property measures 8 mi by 6 mi. find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.