Equation of a Circle

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 center of a circle from its equation?

Back

The center of a circle in the equation (x - h)² + (y - k)² = r² is given by the coordinates (h, k).

Front

What does the radius of a circle represent in its equation?

Back

The radius (r) in the equation (x - h)² + (y - k)² = r² represents the distance from the center of the circle to any point on the circle.

Front

What are congruent circles?

Back

Congruent circles are circles that have the same radius but may be located at different centers.

Front

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

Back

The area (A) of a circle is calculated using the formula A = πr², where r is the radius.

Front

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

Back

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

Front

What is the center and radius of the circle given by the equation (x + 2)² + (y - 3)² = 16?

Back

Center: (-2, 3), Radius: 4 units.

Front

Write the equation of a circle with center (0, 0) and radius 5.

Back

The equation is x² + y² = 25.

Front

What is the distance formula used for in relation to circles?

Back

The distance formula is used to determine the distance between the center of the circle and any point on the circle.

Front

How do 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, the point is inside; if equal, on; if greater, outside.