Find the standard form of the equation of the ellipse with the given characteristics. 10/ 8 (6,8) 4 (5,4) (7,4) 2- (6,0) 2 4 6 8 10 (i)Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.) 2y2 _ X2 = 2 2 Center: (x, y) = 0,0 Vertices: smaller y-value (x, y) = 0, - 1 larger y-value ( x, y ) = 0,1 Foci: smaller y-value (x, y) = X larger y-value ( x, y ) =Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.) 2y2 _ x2 = 2 2 Center: (x, y) = 0,0 Vertices: smaller y-value (x, y) = 0, - 1 larger y-value ( x, y ) = 0,1 Foci: smaller y-value (x, y) = X larger y-value ( x, y) =Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.) 25y2 - x2 + 2x + 150y + 225 = 0 Center: (x, y) = 1, - 3 Vertices: smaller x-value (x, y) = X larger x-value ( x, y) = X Foci: smaller x-value (x, y) = X larger x-value ( x, y) = X Asymptotes: negative slope X positive slope XThe x'y'-coordinate system is rotated 0 degrees from the xy-coordinate system. The coordinates of a point in the xy-coordinate system are given. Find the coordinates of the point in the rotated coordinate system. 0 = 45, (6, 5) ( x' , y ') = X Need Help? Read It Submit AnswerRotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form. (Use xp for x' and yp for y' in your answer. Rotate the coordinate axes through an angle 0 with Oses" xy + 3 = 0 X Sketch the graph of the resulting equation, showing both sets of axes. y 4 10 1 10/