Equations of 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 does the variable 'h' represent in the equation of a circle?

Back

h represents the x-coordinate of the center of the circle.

Front

What does the variable 'k' represent in the equation of a circle?

Back

k represents the y-coordinate of the center of the circle.

Front

If a circle has a center at (3, -2) and a radius of 5, what is its equation?

Back

(x - 3)² + (y + 2)² = 25

Front

What is the radius of a circle if its equation is (x + 1)² + (y - 4)² = 36?

Back

The radius is 6.

Front

How do you find the center of a circle from its equation (x - 2)² + (y + 3)² = 16?

Back

The center is (2, -3).

Front

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

Back

Area = πr², where r is the radius.

Front

What does the equation x² + y² = r² represent?

Back

It represents a circle centered at the origin (0, 0) with radius r.

Front

If the radius of a circle is doubled, how does the area change?

Back

The area increases by a factor of four.

Front

What is the diameter of a circle in relation to the radius?

Back

Diameter = 2 * radius.