The endpoints of a diameter of a circle are (-4,1) and (2,5) . Find the center and radius of the circle. O A. center: (-1,3) ; r = 2V13 O B. center: (-2,2) ; r = 2V13 O C. center: (-1,3) ; r = 13 O D. center: (-2,2); r = V13Which of the following could be the graph of y' -4x- 2y-2=0? O A.O D.The equation that models a portion of an optical lens is 4::3 15y2 +6x8y72 : 0. Which conic section models the shape of this lens? 0 A. circle 0 B. ellipse O C. hyperbola O D. parabola Find the center and radius of the circle represented by the equation (3+2): +(y4)2 :15. O A. center: (-2.4) ;r=4 O B. center: (2,4) ;r=4 O C. center: (2,4) ;r= 4 O D. center: (-2.4) ;r= 16 A circle with a center of (4.5) passes through the point (2,3). What is its equation in standard form? 0 A. (x4)'+(y+5)'=40 O 3- (x4)'+(y+5)'=2o O C. (x+4)'+(y5)'=40 O D. (x+4)'+(y5)' =20 Find the center and radius of the circle represented by the equation x' +y2 -4y8= 0. O A. center: (2.0); r: 26 O B. center: (1,-2) ;r= 5 O C. center: (1.2); r= 6 O D. center: (0.2); 1": 2x5 A GPS satellite can determine if you are within 5 mi. of its position, represented by the point (-2,1) on a grid. If each unit on the grid represents 1 mi., find the equation in standard form of the boundary of this region. O A. (x-2) +(y+1)? = 25 O B. (x-2)' +()+1)? =5 O C. (x+2) +(x-1)? =25 O D. (x+2 )+(x-1)? =5Write the equation of the ellipse with center (2,-3), vertex (2, 1) , and focus (2,-3+ 2V3). O A. ( x-2) () + 3)2 + = 1 2 4 O B. (x-2) + ( y + 3 ) ? = 1 4 2 O C. ( x-2) + ( v + 3 ) ? = 1 4 16 O D. ( x-2) ( )+ 3)2 + = 1 16 4Use the image to answer the question. Write the equation of the ellipse in standard form and identify the foci. \fSuppose a tunnel for a road is in the shape of a semi-ellipse represented by the equation x -= 1, with measurements given in feet. Engineers have 400 144 decided that the tunnel must be twice as wide and 1.5 times as tall. Write the equation that represents the new tunnel. O A. x = 1 800 216 O B. + 600 288 O C. 900 576 O D. + =1 1600 324\fFind the equation for the parabola with vertex (4,6) and focus (4,9) . O A. ( x-4)' = 12(y-6) O B. ( x - 4)' = 3(y-6) O C. (y-6)2 = 3(x-4) O D. (y-6) = 12(x-4)20 15 10 (3,2) -20 -15 -10 10 15 20 5 (3,-2) -10 -15 -20 Use the image to answer the question. Write the equation for the parabola shown.O A. (y-2) = -4(x-3) O B. (y-2) = -16(x-3) O C. ( x -3)? =-4()-2) O D. (x-3 ) = -16(y-2)Identify the focus and directrix of the parabola represented by the equation (y - 2) = 24(x-5). O A. focus: (5,7) ; directrix: y =-4 O B. focus: (5,-4); directrix: y = 7 O C. focus: (11,2) ; directrix: x = -1 O D. focus: (-1,2) ; directrix: x = 11Convert the equation 2y2 -5x+12y +23=0 into standard form. O A. (2y+3)2 = 5(x-1) O B. (y+ 3)? = =(x-1) O C. ( v+ 3 )2 = NIU (x+1) O D. (2y+3)? = 5(x+1)An architect is designing a commemorative steel arch in the shape of a parabola. lta axis is vertical and its feet are 300 yd. apart. If the focus of the parabolic arch is to be 80 yd. above the ground. how high must the arch be? 0 A. wow. 0 B. 125w. O c.144yd. 0 D. 150 yd. Rewrite the equation -9x +4y2-18x-48y+99 =0 in standard form. O A. ( y -6) (x+ 1)? = 1 9 4 O B. ( y -6) (x+ 1)? = 1 4 9 O C. ( y-6) (x- 1) 2 = 1 9 4 O D. ( y-6) (x- 1)2 = 1 4 910 1- 1o (-53, -. (-35 ,-.3)(_ . _3)o 5 2 35035318 -3) ~10 -15 Use the image to answer the question. Write the equation for the hyperbola shown. O A. ( ) + 3) ( x + 3)2 = 1 25 25 O B. (x- 3) 2 ( ) - 3 ) 2 - = 1 25 25 O C. ( y- 3 ) (x- 3)- : 1 25 25 O D. ( x+ 3)2 ( ) + 3 )? = 1 25 25Write the equation of the hyperbole with center (-3.2), vertex (-1.2) . and focus (3+2J.2). 0 A. 0+3)\" (yz)\" Write the equations of the asymptotes for the hyperbola represented by 25x2 -4y' -100x+40y+100 = 0. O A. y= UIN - x and y = -. UIIN -x+4 O B. 21 29 y= UIN x+ and y= UIN x+ 5 5 O C. 21 29 = NIU X - and y = x+ 2 2 O D. y= - x and y = -. 5 - x+10 2A telescope is built using a hyperbolic mirror modeled by the equation ()+1) _(x+1) = 1, and a parabolic mirror that opens downward. The parabola has the 16 9 vertex (-1,-4) and shares a focus with the hyperbola. What are the coordinates of the focus they share? O A. (-1,-4) O B. (4,-1) O C. (-1,-6) O D. (-6,-1)