1 Find the standard form of the equation of the hyperbola satisfying the given conditions. Endpoints of transverse axis: (0, -10), (0, 10); asymptote: y = - - 5 8 x =1 =1 - =1 - =1 Question 2 Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of major axis: (10, -3) and (-2, -3); endpoints of minor axis: (4, -1) and (4, -5) Question 3 + =1 + =1 + =0 + =1 Find the standard form of the equation of the hyperbola satisfying the given conditions. Center: (6, 5); Focus: (3, 5); Vertex: (5, 5) (x - 5)2 - =1 - (y - 6)2 = 1 - (y - 5)2 = 1 (x - 6)2 - =1 Question 4 Find the standard form of the equation of the hyperbola satisfying the given conditions. Endpoints of transverse axis: (-6, 0), (6, 0); foci: (-7, 0), (-7, 0) Question 5 - =1 - =1 - =1 - =1 Identify the equation as a parabola, circle, ellipse, or hyperbola. 9x2 = 4y2 + 36 Circle Parabola Ellipse Hyperbola Question 6 Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis vertical with length 16; length of minor axis = 6; center (0, 0) + + Question 7 =1 =1 + =1 + =1 Find the vertices and locate the foci for the hyperbola whose equation is given. y= vertices: (-2 foci: (-2 , 0), (2 , 0), (2 , 0) , 0) vertices: (-12, 0), (12, 0) foci: (-2 , 0), (2 vertices: (0, -2 foci: (0, -2 , 0) ), (0, 2 ), (0, 2 ) ) vertices: (-12, 0), (12, 0) foci: (-2 , 0), (2 , 0) Question 8 Identify the equation as a parabola, circle, ellipse, or hyperbola. 4x2 = 36 - 4y2 Circle Hyperbola Ellipse Question 9 Find the vertices and locate the foci for the hyperbola whose equation is given. 81y2 - 64x2 = 5184 vertices: (0, -9), (0, 9) foci: (0, - ), (0, ) vertices: (-9, 0), (9, 0) foci: (- , 0), ( , 0) vertices: (0, -8), (0, 8) foci: (0, - ), (0, ) vertices: (-8, 0), (8, 0) foci: (- , 0), ( , 0) Question 10 Find the standard form of the equation of the parabola using the information given. Focus: (3, 3); Directrix: y = -5 (x - 3)2 = 16(y + 1 ) (y - 3)2 = 16(x + 1 ) (y + 1)2 = 16(x - 3 ) (x + 1)2 = 16(y - 3 ) Question 11 Identify the equation as a parabola, circle, ellipse, or hyperbola. 12y = 3(x + 8)2 Hyperbola Ellipse Parabola Circle Question 12 Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. x2 - 6x - 6y - 21 = 0 (x + 3)2 = -6(y + 5 ) (x - 3)2 = 6(y - 5) (x + 3)2 = 6(y + 5) (x - 3)2 = 6(y + 5) Question 13 Identify the equation as a parabola, circle, ellipse, or hyperbola. (x - 2)2 = 16 - y2 Ellipse Hyperbola Circle Parabola Question 14 Convert the equation to the standard form for a hyperbola by completing the square on x and y. 4x2 - 25y2 - 8x + 50y - 121 = 0 - =1 - =1 - =1 - =1 Question 15 Identify the equation as a parabola, circle, ellipse, or hyperbola. 2x = 2y2 - 30 Circle Parabola Ellipse Hyperbola Question 16 Solve the problem. An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 6.25 inches tall and stand 50 inches apart. At some point along the road from the lowest point of the cable, the cable is 1 inches above the roadway. Find the distance between that point and the base of the nearest tower. 15.2 in. 9.8 in. 15 in. 10.2 in. Question 17 Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of major axis: and + =1 + =1 + =1 + =1 ; endpoints of minor axis: and Question 18 Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. y2 - 4y - 2x - 2 = 0 (y - 2)2 = 2(x - 3) (y + 2)2 = 2(x + 3) (y + 2)2 = -2(x + 3 ) (y - 2)2 = 2(x + 3) Question 19 Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis horizontal with length 12; length of minor axis = 6; center (0, 0) + =1 + =1 + =1 + =1 Question 20 Find the standard form of the equation of the parabola using the information given. Focus: (-3, -1); Directrix: x = 7 (y + 1)2 = -20(x - 2 ) (x - 2)2 = -20(y + 1 ) (x + 1)2 = -20(y - 2 ) (y - 2)2 = -20(x + 1 ) Question 21 Solve the problem. An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers stand 40 inches apart. At a point between the towers and 10 inches along the road from the base of one tower, the cable is 1 inches above the roadway. Find the height of the towers. 3.5 in . 4.5 in . 6 in. 4 in. Question 22 Find the standard form of the equation of the parabola using the information given. Vertex: (4, -7); Focus: (3, -7) (x + 4)2 = -16(y - 7 ) (x + 4)2 = 16(y - 7) (y + 7)2 = -4(x - 4) (y + 7)2 = 4(x - 4) Question 23 Convert the equation to the standard form for a hyperbola by completing the square on x and y. 4y2 - 25x2 - 16y + 100x - 184 = 0 Question 24 - =1 - =1 - =1 Find the vertices and locate the foci for the hyperbola whose equation is given. 49x2 - 16y2 = 784 vertices: (0, -4), (0, 4) foci: (0, - ), (0, ) vertices: (-7, 0), (7, 0) foci: (- , 0), ( , 0) vertices: (-4, 0), (4, 0) foci: (- , 0), ( , 0) vertices: (-4, 0), (4, 0) foci: (- , 0), ( , 0) Question 25 Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -3 and 3 + = + = + = 1 1 1 + 1 =