SOLUTION: Find the ellipse 16x^2+25y^2-64x+50y-311=0, find the center, vertices, and foci, and draw a graph.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the ellipse 16x^2+25y^2-64x+50y-311=0, find the center, vertices, and foci, and draw a graph.      Log On


   

Question 310645: Find the ellipse 16x^2+25y^2-64x+50y-311=0, find the center, vertices, and foci, and draw a graph.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square in x and y.
+16x%5E2%2B25y%5E2-64x%2B50y-311=0
+16x%5E2-64x%2B25y%5E2%2B50y-311=0
+16%28x%5E2-4x%29%2B25%28y%5E2%2B2y%29-311=0
+16%28x%5E2-4x%2B4%29%2B25%28y%5E2%2B2y%2B1%29-311=64%2B25
+16%28x-2%29%5E2%2B25%28y%2B1%29%5E2=64%2B25%2B311
+16%28x-2%29%5E2%2B25%28y%2B1%29%5E2=400
+%28x-2%29%5E2%2F25%2B25%28y%2B1%29%5E2%2F16=1
Center : (2,-1)
a: 5
b:4
c:sqrt%285%5E2-4%5E2%29=3