Equation of a circle - Problem so

Front

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

Back

(x - h)² + (y - k)² = r²

Front

How do you find the center of a circle given the endpoints of its diameter?

Back

The center is the midpoint of the diameter, calculated as ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the radius of a circle if the equation is given as (x - h)² + (y - k)² = r²?

Back

The radius r is the square root of the right side of the equation.

Front

If a circle has a center at (0, 0) and a radius of 5, what is its equation?

Back

x² + y² = 25

Front

How can you determine if a point (x, y) lies inside, outside, or on a circle?

Back

Calculate the distance from the point to the center. If d < r, it's inside; if d = r, it's on; if d > r, it's outside.

Front

What is the distance formula used to find the radius of a circle?

Back

d = √((x2 - x1)² + (y2 - y1)²)

Front

What is the significance of the center of a circle in its equation?

Back

The center (h, k) determines the location of the circle in the coordinate plane.

Front

Given the center (-1, 3) and a point (-5, 6), how do you find the radius?

Back

Use the distance formula: r = √((-5 - (-1))² + (6 - 3)²) = √(16 + 9) = 5.

Front

What does the term 'diameter' refer to in a circle?

Back

The diameter is the longest distance across the circle, passing through the center, equal to twice the radius.

Front

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

Back

Complete the square for both x and y terms.