Answer:
[tex]\frac{x^2}{25}+\frac{y^2}{16}=1[/tex]
Step-by-step explanation:
We know that the foci lies on the major axis, so it should lie on the x - axis. Additionally the center is the midpoint of the line joining the foci, at (0,0).
Now remember we have our foci at the point (0, ± 3). Our major axis length is 10, so if covers 5 units on either side of the x - axis. Therefore, c = 3, and a = 5. But remember that c is not part of an ellipse equation. Take a look at the formula below,
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
However we can solve for " b " instead, using c. Take a look at another major formula below,
c^2 = a^2 - b^2,
(3)^2 = (5)^2 - b^2,
9 = 25 - b^2,
- b^2 = 16,
b = 4 = - 4
Whether b = - 4 or b = 4, or equation will be the same.
(x - 0)^2 / (5)^2 + (y - 0)^2 / (4 or - 4)^2 = 1,
x^2 / 25 + y^2 / 16 = 1
Our solution is hence option number 1 : [tex]\frac{x^2}{25}+\frac{y^2}{16}=1[/tex]
