Final answer:
The equation of the ellipse with the given foci and x-intercepts is (x^2/81) + (y^2/17) = 1.
Step-by-step explanation:
To find the equation of an ellipse with foci (-8,0) and (8,0) and x-intercepts (-9,0) and (9,0), we use the standard form of the ellipse equation for a horizontal ellipse which is (x^2/a^2) + (y^2/b^2) = 1.
The distance between the center and the foci (c) is 8, and since the center of an ellipse is in the middle of the foci, the center is at (0,0).
The distance from the center to the x-intercepts (a) is 9. With these, we can find b^2 by the relation c^2 = a^2 - b^2. Substituting the values, we get b^2 = a^2 - c^2 = 9^2 - 8^2 = 81 - 64 = 17.
Thus, the equation of the ellipse is: (x^2/81) + (y^2/17) = 1.