circles

What is the definition of a circle in the xy-plane?

A circle is a set of points in the xy-plane that are a fixed distance r away from a fixed point (h, k).

What is the fixed distance called in the context of circles?

The fixed distance is called the radius.

What is the fixed point called in the context of circles?

The fixed point is called the center of the circle.

What form of an equation represents a circle with radius r and center (h, k)?

The standard form of the equation of a circle is (x - h)² + (y - k)² = r².

What does the point (h, k) represent in the equation of a circle?

The point (h, k) represents the center of the circle.

If the center of the circle is at (0,0) and the radius is 1, what type of circle do we have?

We have a unit circle.

How do you derive the equation of a circle by completing the square?

You rearrange the equation, complete the square for x and y terms, and then express it in standard form.

In the context of circles, what are intercepts?

Intercepts are points where the circle intersects the x-axis and y-axis.

What information is needed to find the equation of a circle?

You need the center coordinates (h, k) and the radius r.

How do you find the center of a circle if given endpoints of a diameter?

The center is the midpoint of the endpoints of the diameter.

The equation of a circle can also be expressed as ______.

(x - h)² + (y - k)² = r².

The center of the circle is represented by the coordinates ______.

(h, k)

In the equation of a circle, the variable r represents the ______.

radius.

The fixed distance from the center to any point on the circle is called the ______.

radius.

If the radius of a circle is doubled, its area is multiplied by ______.

four.

A circle with a radius of 0 is known as a ______.

point.

The distance between the center and a point on the circle is always equal to ______.

the radius.

The standard equation of a circle is derived from ______ the square of the x and y terms.

completing.

In a coordinate plane, a vertical line intersecting a circle will yield ______ axis intercepts.

y.

The circle that has a radius of 1 is called a ______ circle.

unit.