What is the general form of the family of curves for the equation x^2 + y^2 = r^2?
Practice Questions
1 question
Q1
What is the general form of the family of curves for the equation x^2 + y^2 = r^2?
Ellipses
Hyperbolas
Circles
Parabolas
The equation x^2 + y^2 = r^2 represents a family of circles with varying radii (r).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the general form of the family of curves for the equation x^2 + y^2 = r^2?
Solution: The equation x^2 + y^2 = r^2 represents a family of circles with varying radii (r).
Steps: 5
Step 1: Understand the equation x^2 + y^2 = r^2. This is the equation of a circle.
Step 2: Identify the components of the equation. Here, 'x' and 'y' are the coordinates of points on the circle, and 'r' is the radius.
Step 3: Recognize that 'r' can be any positive number. This means the radius of the circle can change.
Step 4: Realize that as 'r' changes, you get different circles. For example, if r=1, you have a circle with radius 1; if r=2, you have a circle with radius 2, and so on.
Step 5: Conclude that the equation x^2 + y^2 = r^2 represents a family of circles, each with a different radius 'r'.
