Checkpoint: Equations of Ellipses Solution

Determine the equation of an ellipse with endpoints $(- 7, 5)$ , $(13, 5)$ , $(3, 17)$ , $(3, - 7)$ . Name the domain and range in interval notation.

$(- 7, 5), (13, 5) (\frac{- 7 + 13}{2}, \frac{5 + 5}{2}) = (\frac{6}{2}, \frac{10}{2}) = (3, 5) d = \sqrt{{(- 7 - 13)}^{2} + {(5 - 5)}^{2}} = 20 Minor axis : \frac{20 a}{2} = 10 (3, 17), (3, - 7) (\frac{3 + 3}{2}, \frac{17 + - 7}{2}) = (3, 5) d = \sqrt{{(3 - 3)}^{2} + {(17 - (- 7))}^{2}} = 24 Major axis : \frac{24 b}{2} = 12$

$\frac{{(x - 3)}^{2}}{100} + \frac{{(y - 5)}^{2}}{144} = 1 Domain [- 7, 13] Range [- 7, 17]$

Note

Q: How do you determine the domain and range interval?

A: Domain: $h - a$ , $h + a$ Range: $k - b$ , $k + b$