If the lengths of the semi-major and semi-minor axes of an ellipse are 5 and 3 respectively, what is the distance between the foci?

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Q: If the lengths of the semi-major and semi-minor axes of an ellipse are 5 and 3 respectively, what is the distance between the foci?

Solution: The distance between the foci is given by 2c, where c = √(a^2 - b^2). Here, c = √(5^2 - 3^2) = √16 = 4, so the distance is 2c = 8.

Steps: 7

Step 1: Identify the lengths of the semi-major and semi-minor axes. Here, the semi-major axis (a) is 5 and the semi-minor axis (b) is 3.
Step 2: Use the formula to find c, which is c = √(a^2 - b^2).
Step 3: Calculate a^2, which is 5^2 = 25.
Step 4: Calculate b^2, which is 3^2 = 9.
Step 5: Subtract b^2 from a^2: 25 - 9 = 16.
Step 6: Take the square root of the result to find c: c = √16 = 4.
Step 7: The distance between the foci is given by 2c. So, calculate 2 * c = 2 * 4 = 8.