10-8 Equations of Circles (Flashcardizz)

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 from the equation of a circle?

Back

To find the radius from the equation (x - h)² + (y - k)² = r², take the square root of r².

Front

What is the center of the circle in the equation (x - 3)² + (y + 4)² = 25?

Back

The center of the circle is (3, -4).

Front

If the radius of a circle is 5, what is the equation of the circle centered at (0, 0)?

Back

The equation is x² + y² = 25.

Front

What is the diameter of a circle if the radius is 2√2?

Back

The diameter is 4√2.

Front

Write the equation of a circle with center (1, -1) and radius 4.

Back

The equation is (x - 1)² + (y + 1)² = 16.

Front

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

Back

The diameter is twice the radius (d = 2r).

Front

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

Back

To convert, complete the square for the x and y terms.

Front

What is the equation of a circle with center (-2, 3) and diameter 10?

Back

The equation is (x + 2)² + (y - 3)² = 25.

Front

In the equation (x + 1)² + (y - 2)² = 9, what is the radius?

Back

The radius is 3.