Equation of a Circle

Front

What is the standard equation of a circle?

Back

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

Front

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

Back

The center of a circle in the equation (x - h)² + (y - k)² = r² is the point (h, k) where the circle is centered.

Front

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

Back

The radius can be found by taking the square root of the value on the right side of the equation in the standard form (x - h)² + (y - k)² = r².

Front

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

Back

The radius is 4, since r² = 16 and r = √16 = 4.

Front

How do you determine if a point lies on a circle?

Back

To determine if a point (x₁, y₁) lies on a circle, substitute x₁ and y₁ into the circle's equation. If the equation holds true, the point lies on the circle.

Front

What is the equation of a circle with center at the origin and radius 5?

Back

The equation is x² + y² = 25.

Front

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

Back

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

Front

Write the equation of a circle with center (3, -2) and radius 3.

Back

The equation is (x - 3)² + (y + 2)² = 9.

Front

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

Back

The distance formula is used to find the distance between the center of the circle and any point on the circle, which should equal the radius.

Front

How can 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.