Find the equation of an ellipse satisfying the given conditions. Foci: $(-5,0)$ and $(5,0)$, length of major axis: 14 The equation of the ellipse is $\square$, (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Step 1 ：Given the foci at $(-5,0)$ and $(5,0)$, and the length of the major axis is 14.

Step 2 ：The semi-major axis \( a \) is half the length of the major axis, so \( a = \frac{14}{2} = 7 \).

Step 3 ：The distance from the center to each focus \( c \) is 5.

Step 4 ：Using the relationship \( c^2 = a^2 - b^2 \), we can find \( b^2 \).

Step 5 ：Substitute the known values to find \( b^2 \): \( 5^2 = 7^2 - b^2 \) which simplifies to \( b^2 = 49 - 25 = 24 \).

Step 6 ：The semi-minor axis \( b \) is the square root of \( b^2 \), so \( b = \sqrt{24} \approx 4.898979485566356 \).

Step 7 ：The equation of the ellipse is \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \).

Step 8 ：Substitute the values of \( a \) and \( b \) into the equation: \( \frac{x^2}{7^2} + \frac{y^2}{24} = 1 \).

Step 9 ：Simplify the equation to get the final answer: \( \boxed{\frac{x^2}{49} + \frac{y^2}{24} = 1} \).