The graph of the equation x^2 + 4y^2 - 10x + 56y = k is a non-degenerate ellipse if and only if k > a. What is a?
Thank you so much!
x^2 -10x + 4y^2 + 56y = k complete the square on x and y
x^2 - 10x + 25 + 4(y^2 + 14y + 49) = k + 25 + 4*49
(x - 5)^2 + 4 ( y + 7)^2 = k + 221
For a non-degenrate ellipse, the right side must be > 0 ....so..... k > -221
So
a = -221
