Match the equation 81y2 - 16x2 = 225 with one of the following graphs. Choose the correct graph below. O A. O B. O c. O D. THTFind the equation of a hyperbola with vertices ( # 4,0) and foci ( # 6,0). Graph the hyperbola. The standard equation for the hyperbola is. (Simplify your answer. Use integers or fractions for any numbers in the equation.) Choose the correct graph below. O A. O B. O C. OD. A XThe equation of a hyperbole is 256x2 yz 1536x 195: + 2295 : 0. :1) Find the center, vertices, transverse axis, and asymptotes of the hyperbole. b) Use the vertices and the asymptotes to graph the hyperbola. a) The center of the hyperbola is . (Type an ordered pair.) The vertices are . (Type an ordered pair. Use a comma to separate answers as needed.) The transverse axis is . (Type an equation.) Determine the equations of the asymptotes. Choose the correct answer below. 1 O A_ y+5= 11(x3) OB. y3=:16(x5) 0Q y+5=:(x73) OD. y+5=i16[x3} b) Choose the correct graph below OA. 12 The equation of a hyperbola is 256x2 -y - 1536x - 10y + 2295 = 0. a) Find the center, vertices, transverse axis, and asymptotes of the hyperbola. b) Use the vertices and the asymptotes to graph the hyperbola. (lype an ordered pair. Use a comma to separate answers as needed.) The transverse axis is ( Type an equation.) Determine the equations of the asymptotes. Choose the correct answer below. O A. y+ 5= 1-(x -3) O B. y - 3= =16(x -5) O c. y+ 5= =(X-3) O D. y+ 5= =16(x -3) b) Choose the correct graph below. O A. O B. O C. OD. 12- Ay 12- Ay 12- 12 JY X X X NO N CO- CO- -123 -12-Find an equation (in standard form) for the hyperbola whose graph is shown to Center Ay the right. (-3,2) . . . Focus Vertex (2,2) The standard equation for the hyperbola is (-6,2) X (Simplify your answer. Use integers or fractions for any numbers in the equation.)