please help with numbers 1 and 2

1. [-/0.12 Points] DETAILS SCALCET8 10.5.AE.003. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Video Example ()) EXAMPLE 3 Find the equation of the ellipse with foci (0, +6) and vertices (0, +7). SOLUTION Using the standard notation, we have c = and a = . Then we obtain b2 = a2 - c2 = 49 - = , so an equation of the ellipse is Another way of writing this equation is 49x2 + 132 = Need Help? Read It 2. [-/0.12 Points] DETAILS SCALCET8 10.5.AE.007. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER EXAMPLE 7 Sketch the conic below and find its foci. 25x2 - 16y2 - 200x + 64y + 736 = 0 SOLUTION We complete the squares as follows. 16(12 - 4y) - 25(x2 - 8x) = 736 16 (1 2 - Ay + - 25 ( x2 - 8 x + = 736 + 64 - 400 16 (1 - ) - 25 ( x - = ( * - 0) (x- D) = 1 Video Example ()) This is in the standard form except that x and y are replaced by x - 4 and y - 2. Thus a2 = | |, 62 = | |, and c2 = |) . The hyperbola is shifted four units to the right and two units upward. The foci are (x, y) = ( and (4, 2 - v41) and the vertices are (x, y) =( and (4, -3). The asymptotes are y - 2 = 1 - (x - 4). The hyperbola is sketched in the figure. Need Help? Read It