Write an equation for an ellipse that has foci at (19,3) and (-7,3), with the length of the major axis being 30.

Question

I just need the thorough steps. Thank you. I need a, b, h, k, etc.

Answer 1

2c = 19 - (-7) = 26; c = 13; 2a = 30; a = 15; b² = 15² - 13² = 225 - 169 = 56.

Center of ellipse x_C = (19 + (- 7))/2 = 6 and y_C = (3 + 3)/2 = 3. So, center C(6, 3).

Equation of ellipse: (x - 3)²/225 + (y - 3)²/56 = 1