Find the distance between the points (4.3) and (11) . Express your answer in simplest radical form. (1 point) ONTO What conic section is represented by the equation 3x2 + 2y -24x+30 = 0? Explain. (4 points)Find the center and radius of the circle represented by the following equation: x" +(y+4)2 = 3_ (1 point) 0 center: (0,4); r: J; 0 center: (0,4) ; r: 3 0 center: (0,4) ; ,:J 0 center: (0,4) ;r = 3 The equation of a circle in general form is x2 +y2 + 6x4y+4 = 0 . Write the equation in standard form. (1 point) 0 (x+3)'+o2)"=4 0 (H3)2 + (y 2)2 = 9 O (x+3)'+(y+2)' :4 0 (H3)2 + 0+2}? = 9 Use the graph to answer the question. Write the standard form of the equation of the circle shown in the graph. (1 point) 0 (x3)2+(y+2)"=3 o (x+3)2+(y2)2=3 o [x3)2+(y+2)2=9 0 ("333+ (yz)2 =9 -10 Write the equation of the ellipse with center (53) , vertex (13,3). and focus (5+ 24,113). (1 point) 0 (rage3)" :1 8 64 O crane3)" =1 8 8 O crane3)" =1 64 8 2 2 O (xS) +014) :1 64 56 Use the graph to answer the question. Write the standard form equation of the ellipse shown in the graph. and identify the foci. (1 point) , (2,3i2 5) , (2,3i 2 5) Is the ellipse represented by the equation ( x - 5 ) ( y+ 1)2 -= 1 oriented horizontally or vertically? Explain how you know. 3 5 (4 points) BI U E(Jr+0.9)2 + y2 12.96 12.15 focus and its coordinates are (0.0) , find Pluto's farthest distance from the sun in billions of miles. The equation that models Pluto's elliptical orbit around the sun is :1 in billions of miles. If the sun is located at one (1 point) 0 13.86 billion mi. O 12.05 billion mi. 0 4.50 billion mi. O 2.70 billion mi. The equation of an ellipse is 41:2 +y2 +10y +13 = 0. Write the equation in standard form. (1 point) x" +(y+5)2 4 12 3 12 + 12 3 1 Find the equation of the parabola with vertex (1.3) and focus [5,3]. (1 point) Identify the focus and directrix of the parabola whose equation is (y-3)? = -4(x-5). (1 point) O focus: (4,2) ; directrix: y = 4 O focus: (4,4) ; directrix: y = 2 O focus: (4,3) ; directrix: x = 6 O focus: (6, 3) ; directrix: x = 4A parabolic microphone used on the sidelines of a professional football game uses a reflective dish 16 in. wide and 4 in. deep. How far from the bottom of the dish should the microphone be placed? (1 point) 0 3in. O 3.2 in. O 3.8in. O 4in. Write the equation of the hyperbola with center (2,-5) , vertex (2,-2) , and focus (2,-5+2~/3) . (1 point) 0 (+5)2 ( x-2) = 1 9 3 0 (+5)2 ( x-2) = 1 9 12 o (+5)2 (x-2) 3 =1 9 0 (+5)2 (x- 2)? = 1 12 9A hyperbole is represented by the equation : (y_4)2 :1. Identify the asymptotes Of the graph. 16 7 (1 point) C) y=E(x+4) and y= E(x+4) 7 7 16 16 =x+4 and = x+4 O y 7 y 7 O y=x+4 and y=x+4 O y=(x+4) and y=(x+4)