6.3.1 Circle Equations

Front

What is the standard equation of a circle centered at (h, k) with radius r?

Back

The standard equation is (x - h)² + (y - k)² = r².

Front

How do you determine if a point (x, y) is inside, on, or outside a circle given by the equation (x - h)² + (y - k)² = r²?

Back

Calculate the distance from the point to the center (h, k). If the distance < r, the point is inside; if = r, it's on the circle; if > r, it's outside.

Front

What is the center and radius of the circle given by the equation x² + y² = 49?

Back

Center: (0, 0), Radius: 7.

Front

Given the circle equation (x - 6)² + (y - 11)² = 144, what is the center and radius?

Back

Center: (6, 11), Radius: 12.

Front

How do you find the diameter of a circle if you know the radius?

Back

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

Front

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

Back

The diameter is always twice the length of the radius.

Front

What is the equation of a circle with center (13, -5) and diameter 8?

Back

The equation is (x - 13)² + (y + 5)² = 16.

Front

How can you determine the distance from a point to the center of a circle?

Back

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What does it mean for a point to be 'outside' a circle?

Back

It means the distance from the point to the center of the circle is greater than the radius.

Front

What does it mean for a point to be 'inside' a circle?

Back

It means the distance from the point to the center of the circle is less than the radius.