Standard Form of Circles

Front

What is the standard form of a circle's equation?

Back

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

Front

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

Back

The center of a circle in standard form (x - h)² + (y - k)² = r² is identified as the point (h, k).

Front

What does the radius represent in the standard form of a circle?

Back

The radius (r) in the standard form of a circle represents the distance from the center of the circle to any point on its circumference.

Front

Convert the center-radius form of a circle to standard form: Center (2, -3), Radius 4.

Back

(x - 2)² + (y + 3)² = 16.

Front

What is the general form of a circle's equation?

Back

The general form of a circle's equation is x² + y² + Dx + Ey + F = 0.

Front

How do you convert from standard form to general form for a circle?

Back

Expand (x - h)² + (y - k)² = r² to get x² + y² - 2hx - 2ky + (h² + k² - r²) = 0.

Front

Identify the center and radius from the equation (x + 1)² + (y - 6)² = 36.

Back

Center: (-1, 6) and radius: 6.

Front

What is the radius of a circle if its equation is (x - 3)² + (y + 2)² = 25?

Back

The radius is 5, since r² = 25.

Front

If a circle's equation is x² + y² - 9 = 0, what is its center and radius?

Back

Center: (0, 0) and radius: 3.

Front

What is the significance of the values h and k in the standard form of a circle?

Back

The values h and k represent the x and y coordinates of the center of the circle, respectively.