Circles in the Coordinate Plane

Front

What is the standard form of the equation of a circle?

Back

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

How do you find the radius of a circle from its equation?

Back

To find the radius, identify the equation in the form (x - h)² + (y - k)² = r². The radius is the square root of r².

Front

What is the center of the circle in the equation (x - 2)² + (y + 3)² = 16?

Back

The center of the circle is (2, -3).

Front

What does the term 'radius' refer to in a circle?

Back

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

Front

What is the diameter of a circle?

Back

The diameter is twice the length of the radius, or the distance across the circle through the center.

Front

How do you convert the general form of a circle's equation to standard form?

Back

To convert, complete the square for the x and y terms in the general form Ax² + Ay² + Bx + Cy + D = 0.

Front

What is the equation of a circle with center (0, 0) and radius 5?

Back

The equation is x² + y² = 25.

Front

What is the significance of the value on the right side of the equation in a circle's equation?

Back

The value on the right side (r²) represents the square of the radius of the circle.

Front

How can you determine if a point lies inside, on, or outside a circle?

Back

Substitute the point's coordinates into the circle's equation. If the result is less than r², it's inside; equal to r², it's on; greater than r², it's outside.

Front

What is the relationship between the radius and the area of a circle?

Back

The area A of a circle is given by the formula A = πr², where r is the radius.