Finding the Center-Radius Form of the Equation of a Circle (3.4.1)

Question 1

• A circle is the set of all points on a plane which are the same distance from a given point, the center of the circle.

Answer 1

• A circle is the set of all points on a plane which are the same distance from a given point, the center of the circle.

Question 2

• The center of a circle is usually given as the ordered pair (h, k) where h is the x-value and k is the y-value of the centerpoint.

Answer 2

• The center of a circle is usually given as the ordered pair (h, k) where h is the x-value and k is the y-value of the centerpoint.

Question 3

• Any point (x, y) mentioned in relation to a circle is found on the circumference of the circle.

Answer 3

• Any point (x, y) mentioned in relation to a circle is found on the circumference of the circle.

Question 4

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

Answer 4

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

Question 5

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

Answer 5

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

Question 6

This diagram shows the major parts of a circle.
You can find the length of the radius by using the distance
formula with the endpoints (h, k) and (x, y).
When you are given the center and the radius, creating the
equation for the circle is a matter of substituting into the
standard equation for a circle. Here, you’re given the center
(h, k) is (–2, 3), so we substitute –2 for h and 3 for k into the
equation.
Notice: The signs change because h and k are subtracting in
the standard equation. You are given the radius is 5 so you
substitute that into the equation and square it.The graph shows
a sketch of the circle.

Answer 6

This diagram shows the major parts of a circle.
You can find the length of the radius by using the distance
formula with the endpoints (h, k) and (x, y).
When you are given the center and the radius, creating the
equation for the circle is a matter of substituting into the
standard equation for a circle. Here, you’re given the center
(h, k) is (–2, 3), so we substitute –2 for h and 3 for k into the
equation.
Notice: The signs change because h and k are subtracting in
the standard equation. You are given the radius is 5 so you
substitute that into the equation and square it.The graph shows
a sketch of the circle.