Circles

Front

What is the standard equation of a circle with center (h, k) and radius r?

Back

(x - h)² + (y - k)² = r²

Front

What is the radius of a circle defined by the equation (x + 4)² + (y - 1)² = 25?

Back

5

Front

How do you find the center of a circle from its equation in standard form?

Back

The center (h, k) can be found from the equation (x - h)² + (y - k)² = r².

Front

What is the diameter of a circle if its radius is 7?

Back

14

Front

If the center of a circle is at (0, 0) and the radius is 10, what is the equation of the circle?

Back

x² + y² = 100

Front

What is the distance between the center of the circle (2, 3) and the point (5, 7)?

Back

5 units

Front

What does the term 'circumference' refer to in relation to a circle?

Back

The circumference is the distance around the circle, calculated as C = 2πr.

Front

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

Back

Area = πr² = 28.27 (approximately) square units.

Front

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

Back

Complete the square for both x and y terms.

Front

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

Back

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