What is the standard form of the equation of a circle whose diameter is 3 units and whose center is (2, 4)? Drag an expression or value to the boxes to correctly complete the equation. What are the lengths of the major and minor axes of the ellipse? (33)\" we)\" _ 27 + 45 _1 Drag a value to the boxes to correctly complete the table. Length of major axis Length of minor axis wwwmww How does the value of the eccentricity of the ellipse describe its shape? 3 :2 '92 _ E+?1 Select answers from the drop-down menus to correctly complete the statements. The eccentricity ofthe ellipse is approximately - This value indicates that the ellipse is more The center of a hyperbola is (3, 2). The length of the conjugate axis is 8 units, and the length of the transverse axis is 12 units. The transverse axis is parallel to the xaxis. What is the equation of the hyperbola in standard form? A Drag an expression to the boxes to correctly complete the equation. (9-2)? (2+3? {st2}\" n+3)\" 16 16 35 36 What are the coordinates of the foci of the hyperbola? (y-6)2 _(I+4) 9 = 1 16 Enter your answer by filling in the boxes. andThe general form of a parabola is x2 - 6x - 2y + 7 = 0. What is the standard form of this parabola? Enter your answer by filling in the boxes.\fL -8 - 2 2 7. 6 -4 -3 -1 2 3 5 6 -1 5 -2 O O -3 3 -4 2 -5 -6 -3 -2 2 3 5 -8 -2Fencing encloses a rectangular backyard that measures 200 feet by 800 feet. A blueprint of the backyard is drawn on the coordinate plane so that the rectangle has vertices (0, 0) , (0, 40) , (10, 40), and (10, 0). A circular flower garden is dug to be exactly in the center of the backyard, with a radius of 60 feet. This garden is represented on the blueprint What is the equation of the flower garden represented on the blueprint? Enter your answer by filling in the boxes.The general form of an ellipse is 1532 + 43,12 l 30:1: 16y 29 = D. What is the standard form of the ellipse? (21)\" (42)\" _ O 15 __ 4 _1 (21)\" (#2)\" O 15 _ 4 =1 n+1)\" (42)\" 0 4 _ 15 =1 (21)\" (42)\" 0 4 _ 15 =1 What is the center of the hyperbola? (y+3)2 (1-7) 9 2 1 Enter your answer by filling in the boxes. center:Kain graphs the hyperbola ( y + 2) 2 (+5)2 64 36 =1 How does he proceed? Drag a value, phrase, equation, or coordinates in the boxes to correctly complete the statements. Kain first identifies the center of the hyperbola as and that the hyperbola opens Since a = the coordinates of the vertices are The slopes of the asymptotes of this parabola are and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are Once this information is gathered, the asymptotes are graphed as dashed lines, and the hyperbola is drawn through theThe slopes of the asymptotes of this parabola are and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are Once this information is gathered, the asymptotes are graphed as dashed lines, and the hyperbola is drawn through the vertices, approaching the asymptotes. (-5, -2) (-2, -5) up and down left and right 6 8 y + 2 =+3 (2+5 ) 3 (a + 5) (-5,6) and (-5, -10) (3, -2) and (-13, -2)The endpoints of a diameter of a circle are (6, 2) and (-2, 5). 12 What is the standard form of the equation of this circle? Enter your answer by filling in the boxes. Enter any fractions in simplified form.The vertex of a parabola is (6, 2), and the equation of its directrix is y = 4. 13 What is the equation of this parabola in standard form? O (y -2)2 = -8(2-6) O (2 -6)2=-8(y-2) O (2 -6)2 -8(y-2) O (y -2)2 -8(2-6)The center of an ellipse is (1, 6). One focus of the ellipse is (-1, 6). One vertex of the ellipse is (6, 6). What is the equation of the ellipse in standard form? 14 Drag an expression into the boxes to correctly complete the equation. = 1 (x-1)2 (y-6)2 21 (z-1)2 21 (y-6)2 25 (y-6)2 4 (z-1)2 25 4The system of conics has two solutions. (ac - 2)' + (y - 3)2 =16 15 (1-2) _ (3-3)2 16 64 =1 What are the solutions to this system of conics? Enter your answer by filling in the boxes. and1. Graph the ellipse. (x + 3)= (1 - 4)2 - = 1 4 16 Name the coordinates of the center, endpoints of major axis, endpoints of minor axis, and foci of the ellipse. Answer: 162. NAROL is a long range hyperbolic navigation system. Suppose two NAROL transmitters are located at the coordinates (-200, 0) and (200, 0), where unit distance on the coordinate plane is measured in miles A receiver is located somewhere in the first quadrant. The receiver computes that the difference in the distances from the receiver to these transmitters is 160 miles. What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola? Answer: 173. A satellite telescope has a parabolic dish. Satellite signals are collected at the focal point (focus) of the parabola. The distance from the vertex of the parabolic dish to the focus is 40 feet. The vertex of the dish is located at a point 50 feet above the ground and 100 feet to the east of a computer that reads and records data from the telescope. The diameter of the dish is 160 feet. What is the depth of the parabolic dish? Answer: fWhat are the points of intersection between the graphs of the circle and parabola? $2+y2=5 92:331 Select all correct coordinates. (2, 1] [1 (3, 2) D (3, 2} [1(2, 1) Hem.r many points of intersection are there between the graphs of the two hyperbelas? 3x25y2+5x7y+2=0 3w22y2+5my+2=0 O 0 O 1 O 2 O4 The graphs of the conics intersect at two points. x2 +y2 = 9 y2 - x2 =1 21 What are the coordinates of these points of intersection? Enter your answer by filling in the boxes. andWhat are the solutions to the system of conics? y - 4 = 1 yz = 8(x+ 1) Drag the ordered pairs into the box to correctly complete the table. Solutions to the system of conics (2 + V6,-216+2V6 (2 + 16, 216+2V6 (2 - V6,-216-2V6 (2 - V6, -2V6+2V6 2 - V6,26 +2V6 (2 - V6,2 6 -2V6 2 + V6,-216-2V6 (2 + 16, 216-2V6