The family of curves represented by the equation x^2 + y^2 = r^2 describes which

₹0.0

Question: The family of curves represented by the equation x^2 + y^2 = r^2 describes which geometric shape?

Options:

Correct Answer: Circle

Solution:

The equation x^2 + y^2 = r^2 represents a circle with radius r.

The family of curves represented by the equation x^2 + y^2 = r^2 describes which geometric shape?

The family of curves represented by the equation x^2 + y^2 = r^2 describes which geometric shape?

Step 1: Look at the equation given: x^2 + y^2 = r^2.
Step 2: Identify the parts of the equation. Here, 'x' and 'y' are variables, and 'r' is a constant that represents the radius.
Step 3: Recognize that this equation is in the standard form of a circle's equation, which is x^2 + y^2 = radius^2.
Step 4: Conclude that since the equation matches the standard form, it describes a circle.
Step 5: Note that 'r' is the radius of the circle, meaning the distance from the center of the circle to any point on its edge.

Circle Equation – The equation x^2 + y^2 = r^2 is the standard form of a circle's equation in a Cartesian coordinate system, where r represents the radius.