Circles

Front

What is the standard equation of a circle?

Back

(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

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

Back

Rearrange the equation to the standard form and identify (h, k) from (x - h)² + (y - k)² = r².

Front

What does the radius (r) represent in the equation of a circle?

Back

The radius (r) is the distance from the center of the circle to any point on the circle.

Front

Write the equation of a circle with center (0, 0) and radius 5.

Back

x² + y² = 25.

Front

What is the center of the circle given by the equation x² + y² - 6x + 4y - 12 = 0?

Back

(3, -2).

Front

How do you complete the square for the equation x² + 4x + y² - 8y = 0?

Back

(x + 2)² + (y - 4)² = 20.

Front

What is the radius of the circle defined by the equation (x - 1)² + (y + 3)² = 16?

Back

4.

Front

Determine the center and radius of the circle given by x² + y² + 6x - 10y + 9 = 0.

Back

Center: (-3, 5), Radius: 5.

Front

What is the effect of changing the value of h in the equation (x - h)² + y² = r²?

Back

It shifts the circle horizontally along the x-axis.

Front

What happens to the circle if the radius (r) is increased?

Back

The circle expands and becomes larger.