Circles: Write the equation from a graph

Front

What is the standard equation of a circle?

Back

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

Front

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

Back

The center of a circle in the equation (x - h)² + (y - k)² = r² is given by the point (h, k).

Front

What does the radius of a circle represent in its equation?

Back

The radius r in the equation (x - h)² + (y - k)² = r² represents the distance from the center (h, k) to any point on the circle.

Front

If the equation of a circle is (x + 3)² + (y - 2)² = 16, what is the center and radius?

Back

The center is (-3, 2) and the radius is 4.

Front

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

Back

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

Front

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

Back

To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for x and y.

Front

What is the significance of the value on the right side of the equation (x - h)² + (y - k)² = r²?

Back

The value on the right side (r²) represents the square of the radius, indicating the size of the circle.

Front

How can you identify if a point lies inside, on, or outside a circle?

Back

Substitute the point (x, y) into the circle's equation. If the result is less than r², it's inside; equal to r², it's on; greater than r², it's outside.

Front

What is the equation of a circle with center at (0, 0) and radius 5?

Back

The equation is x² + y² = 25.

Front

What does it mean if the radius squared (r²) is negative in a circle's equation?

Back

A negative r² indicates that the equation does not represent a real circle; it has no real solutions.