Circle Functions

The equation of a circle is , in which (h, k) is the center of the circle. To derive the center of a circle from its equation, identify the constants immediately following x and y, and flip their signs. In the given equation, x is followed by -1 and y is followed by -6, so the coordinates of the center must be (1, 6).

The equation given represents a circle.

represents the center, and is the radius.

The center is at:

Set up an equation to solve the radius.

The radius is:

The answer is:

The equation given represents a circle.

represents the center, and is the radius.

The center is at:

Set up an equation to solve the radius.

The radius is:

The answer is:

Remember that the "shifts" involved with circular functions are sort of like those found in parabolas. When you shift a parabola left or right, you have to think "oppositely". A right shift requires you to subtract from the x-component, and a left one requires you to add. Hence, this circle has no horizontal shift, but does shift 6 upward for the vertical component.

You can also remember the general formula for a circle with center at and a radius of .

Comparing this to the given equation, we can determine the center point.

The center point is at (0,6) and the circle has a radius of 5.

Remember that the "shifts" involved with circular functions are sort of like those found in parabolas. When you shift a parabola left or right, you have to think "oppositely". A right shift requires you to subtract from the x-component, and a left one requires you to add. Hence, this circle has no horizontal shift, but does shift 6 upward for the vertical component.

You can also remember the general formula for a circle with center at and a radius of .

Comparing this to the given equation, we can determine the center point.

The center point is at (0,6) and the circle has a radius of 5.

The equation of a circle is , in which (h, k) is the center of the circle. To derive the center of a circle from its equation, identify the constants immediately following x and y, and flip their signs. In the given equation, x is followed by -1 and y is followed by -6, so the coordinates of the center must be (1, 6).

First determine the center of the circle. The "x-3" portion of the circle equation tells us that the x coordinate is equal to 3. The "y-3" portion of the circle equation tells us that the y coordinate is equal to 3 as well. Therefore, the center of the circle is at (3,3).

To find the distance between (3,3) and (0,0), it is necessary to use the Pythagorean Theorem . Where "a" and "b" are equal to 3

(to visualize, you may draw the two points on a graph, and create a triangle. The line connecting the two points is the hypotenuse, aka "c." )

First determine the center of the circle. The "x-3" portion of the circle equation tells us that the x coordinate is equal to 3. The "y-3" portion of the circle equation tells us that the y coordinate is equal to 3 as well. Therefore, the center of the circle is at (3,3).

To find the distance between (3,3) and (0,0), it is necessary to use the Pythagorean Theorem . Where "a" and "b" are equal to 3

(to visualize, you may draw the two points on a graph, and create a triangle. The line connecting the two points is the hypotenuse, aka "c." )

First, recall what the standard equation of a circle: . Your center is (h,k). Remember to flip the signs to get your center for this equation: .

To convert the given equation into the format , complete the square by adding to the x-terms and to the y-terms.

The square root of 4 is 2, so the radius of the circle is 2.