Question

What is the equation of an ellipse centered at (4,-1) having a horizontal minor axis of length 14 and a major axis of length 20?

Answer 1

an ellipse with center at the origin (0,0) is the graph of \[\frac{ x^2 }{ a^2 } + \frac{ y^2 }{ b^2 } = 1 or \frac{ x^2 }{ b^2 }+\frac{ y^2 }{ a^2 }=1 \]

Answer 2

The length of the major axis is 2a, and the length of the minor axis is 2b. The two foci (foci is the plural of focus) are at (± c , 0) or at (0 , ± c), where c2 = a2 - b2.