Geometry Unit 6 Circles Test Review

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 of the circle and r is the radius.

Front

How do you find the radius of a circle given its diameter?

Back

The radius is half the diameter. If the diameter is d, then the radius r = d/2.

Front

What is the relationship between a tangent line and a radius at the point of tangency?

Back

A tangent line is perpendicular to the radius at the point of tangency.

Front

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

Back

To convert to standard form, complete the square for the x and y terms in the equation 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

If a circle has a center at (-3, 4) and a radius of 7, what is its equation?

Back

The equation is (x + 3)² + (y - 4)² = 49.

Front

What is the formula for the circumference of a circle?

Back

The circumference C of a circle is given by C = 2πr, where r is the radius.

Front

What is the area of a circle with a radius of 3?

Back

The area A of a circle is A = πr². For r = 3, A = 9π.

Front

How do you find the perimeter of a semicircle?

Back

The perimeter P of a semicircle is P = πr + 2r, where r is the radius.

Front

What is the distance formula used for in geometry?

Back

The distance formula is used to find the distance between two points (x₁, y₁) and (x₂, y₂): d = √((x₂ - x₁)² + (y₂ - y₁)²).