If an ellipse has a semi-major axis of 10 and a semi-minor axis of 6, what is th

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Question: If an ellipse has a semi-major axis of 10 and a semi-minor axis of 6, what is the value of b^2?

Options:

Correct Answer: 36

Solution:

For an ellipse, b is the semi-minor axis. Here, b = 6, so b^2 = 6^2 = 36.

If an ellipse has a semi-major axis of 10 and a semi-minor axis of 6, what is the value of b^2?

If an ellipse has a semi-major axis of 10 and a semi-minor axis of 6, what is the value of b^2?

Step 1: Understand that in an ellipse, the semi-major axis is the longer radius and the semi-minor axis is the shorter radius.
Step 2: Identify the given values: the semi-major axis is 10 and the semi-minor axis is 6.
Step 3: Recognize that 'b' represents the semi-minor axis in the equation of an ellipse.
Step 4: Since the semi-minor axis is given as 6, we have b = 6.
Step 5: To find b^2, we need to square the value of b. So, calculate 6^2.
Step 6: Perform the calculation: 6^2 = 36.
Step 7: Conclude that the value of b^2 is 36.

Ellipse Properties – Understanding the definitions of semi-major and semi-minor axes in the context of an ellipse.
Mathematical Operations – Performing basic arithmetic operations, specifically squaring a number.