What is the general form of the family of curves represented by the equation x^2

₹0.0

Question: What is the general form of the family of curves represented by the equation x^2 + y^2 = r^2?

Options:

Correct Answer: Circles with radius r

Solution:

The equation x^2 + y^2 = r^2 represents a family of circles with radius r centered at the origin.

What is the general form of the family of curves represented by the equation x^2 + y^2 = r^2?

What is the general form of the family of curves represented by the equation x^2 + y^2 = r^2?

Correct Answer: Circles with radius r centered at the origin.

Step 1: Understand the equation x^2 + y^2 = r^2. This is a mathematical equation.
Step 2: Recognize that 'x' and 'y' are variables that represent points on a graph.
Step 3: Identify 'r' as a constant that represents the radius of a circle.
Step 4: Note that the equation describes all points (x, y) that are a distance 'r' from the center.
Step 5: Understand that the center of the circle is at the point (0, 0) on the graph.
Step 6: Conclude that the equation represents a circle with radius 'r' centered at the origin.

No concepts available.