Find the distance between the points (4,3) and (2,-1) . Express your answer in simplest radical form. O A. 2V10 O B. 2V5 O C. 2V/3 O D. 212What conic section is represented by the equation 3x+ 2y -24x+30=0? Explain.Find the center and radius of the circle represented by the following equation: x' +(y+6)' = \"I . O A. center: (0,6); r= 7 O B. center: (0,6); r=1 O C. center: (0,6) ; r= 7 O D. center: (0,6); r= The equation of a circle in general form is x3 +y +4x-6y+9=0. Write the equation in standard form. O A. ( x+ 2)+ (y - 3)2 = 4 O B. ( x + 2 )?+ ( y - 3)2 =9 O C. ( x + 2) + (y+ 3)2 =4 O D. ( x + 2 )+ ( y+ 3)2 = 9Use the graph to answer the question. Write the standard form of the equation of the circle shown in the graph. O A. (x+4)' + (y - 3)? =2 O B. (x-4)2 + (y + 3)? = 2 O C. (x+4)' + (y-3)? =4 O D. (x-4)' + ()+3)? =4Write the equation of the ellipse with center (4.2), vertex (9,2), and focus (4+2J,2). O A- (My (yz)' Use the graph to answer the question. Write the standard form equation of the ellipse shown in the graph, and identify the foci. \f3 3 Is the ellipse represented by the equation +=1 oriented horizontally or vertically? Explain how you know. 3 5 A The equation that models Pluto's elliptical orbit around the sun is (x+0.9) = 1 in billions of miles. If the sun is located at one focus and its coordinates 12.96 12.15 are (0,0), find Pluto's farthest distance from the sun in billions of miles. O A. 13.86 billion mi. O B. 12.06 billion mi. O C. 4.50 billion mi. O D. 2.70 billion mi.The equation of an ellipse is 4.1:2 +y2 +10y+13 = 0. Write the equation in standard form. 0 A. i+(y+5)'=1 4 3 O 2 B. +(y+5) =1 4 12 O 2 C. +(y+5) =1 3 12 OD. (y+5)2 =1 1+ 12 3 Find the equation of the parabola with vertex (1,3) and focus , 3 O A. (y- 3) =-2(x-1) O B. (y-3) = 2(x-1) O C. (x-1 ) = -2(y-3) O D. ( x-1) = 2(y -3)Identify the focus and directrix of the parabola whose equation is (y -1) = -8(x-4) . O A. focus: (4,3) ; directrix: y = -1 O B. focus: (4,-1) ; directrix: y = 3 O C. focus: (6,1) ; directrix: x = 2 O D. focus: (2, 1) ; directrix: x = 6A parabolic microphone used on the sidelines of a professional football game uses a reflective dish 20 in. wide end 5 in. deep. How far from the bottom of the dish should the microphone be placed? 0 A. 4in. O B. 4.6in. O C. 4.8m. O D. 5in. Note: Remember to show all of the steps that you use to solve the problem. Be sure to use the text box where the question mark (?) first appears to show your mathematical work. You can use the comments field to explain your work. Your teacher will review each step of your response to ensure you receive proper credit for your answer. Write the equation -4x3 +9y' +32x+36y-64=0 in standard form. Show each step of the process. Math symbols Relations Geometry Groups Trigonometry StatisticsWhich is the graph of the following equation? (x- 5)2 (y-2)? = 1 16 9 O A. 10 cn x OT 5 10 15 5O D. 15 10 0- -15 -10 -5 10 15 -5 -10 -15Write the equation of the hyperbola with center (2,-5) , vertex (2,-2) , and focus (2,-5+21/3) . O A. ()+5)3 ( x-2)2 = 1 9 3 O B. (v+5)2 (x- 2)? = 1 9 12 O C. (v+ 5)2 (x-2)2 - =1 3 9 O D. (v+ 5)2 (x-2) - =1 12 9A hyperbola is represented by the equation (y-2)? =1 . Identify the asymptotes of the graph. 4 3 O A. y= - x+2 and y= -- x+2 4 4 O B. 3 y= x +2 and y = - x+2 2 2 O C. 3 y= - (x+2) and y= - AIW (x + 2) 4 O D. V3 (x+2) and y = -_ V3 (x + 2) 2 2