The standard equation for an ellipse is
where
(h,k) = coordinates of the center
a, b = semi-major and semi-minor axes
Refer to the figure shown below.
The center of the ellipse is at (0,0).
Therefore, h=0, k=0.
One focus is at (12, 0)
Therefore
c = 12
One directrix is at 14 1/12 = 169/12.
Because the directrix is located at x = a²/c, therefore
a²/12 = 169/12
a² = 169/144
a = 13
Because c² = a² - b², obtain
b² = a² - c²
= 169 - 144 = 25
b = 5
Answer:
The equation for the ellipse is
where
(h,k) = coordinates of the center
a, b = semi-major and semi-minor axes
Refer to the figure shown below.
The center of the ellipse is at (0,0).
Therefore, h=0, k=0.
One focus is at (12, 0)
Therefore
c = 12
One directrix is at 14 1/12 = 169/12.
Because the directrix is located at x = a²/c, therefore
a²/12 = 169/12
a² = 169/144
a = 13
Because c² = a² - b², obtain
b² = a² - c²
= 169 - 144 = 25
b = 5
Answer:
The equation for the ellipse is