What type of curves does the equation (x^2/a^2) + (y^2/b^2) = 1 represent?

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Question: What type of curves does the equation (x^2/a^2) + (y^2/b^2) = 1 represent?

Options:

Correct Answer: Ellipses

Solution:

The equation (x^2/a^2) + (y^2/b^2) = 1 represents a family of ellipses with varying semi-major (a) and semi-minor (b) axes.

What type of curves does the equation (x^2/a^2) + (y^2/b^2) = 1 represent?

What type of curves does the equation (x^2/a^2) + (y^2/b^2) = 1 represent?

Step 1: Identify the equation given: (x^2/a^2) + (y^2/b^2) = 1.
Step 2: Recognize that this equation is in the standard form of an ellipse.
Step 3: Understand that 'a' represents the semi-major axis (the longer part of the ellipse).
Step 4: Understand that 'b' represents the semi-minor axis (the shorter part of the ellipse).
Step 5: Conclude that the equation describes a family of ellipses, which can vary in size depending on the values of 'a' and 'b'.

No concepts available.