Decoding the Circle Formula (3.4.3)

Question 1

• Equation of a circle: (x – h)^2 + (y – k)^2 = r^2

Answer 1

• Equation of a circle: (x – h)^2 + (y – k)^2 = r^2

Question 2

• The center of a circle is represented by the point (h, k).

Answer 2

• The center of a circle is represented by the point (h, k).

Question 3

• The radius is the distance from the center of a circle to any point on its circumference.

Answer 3

• The radius is the distance from the center of a circle to any point on its circumference.

Question 4

When you first look at an equation, a natural question is what kind of line or curve is it representing.
An equation that has an x^2 and a y^2 with terms being added together positively will likely be a circle.
When defining the center of the circle remember to change the signs from the standard form of the equation. The equation states (x – h) and (y – k), showing both center values as negative, while the ordered pair (h, k) shows both values as positive. The radius will be the square root of the constant on the right side of the equation. It will always be positive because it represents a distance. And once you know the center and the radius of a circle, you can easily sketch its graph.

Answer 4

When you first look at an equation, a natural question is what kind of line or curve is it representing.
An equation that has an x^2 and a y^2 with terms being added together positively will likely be a circle.
When defining the center of the circle remember to change the signs from the standard form of the equation. The equation states (x – h) and (y – k), showing both center values as negative, while the ordered pair (h, k) shows both values as positive. The radius will be the square root of the constant on the right side of the equation. It will always be positive because it represents a distance. And once you know the center and the radius of a circle, you can easily sketch its graph.