Conics- Circles

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 find the radius of a circle from its equation?

Back

The radius can be found by taking the square root of the right side of the equation in the standard form (x - h)² + (y - k)² = r².

Front

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

Back

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

Front

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

Back

The equation is x² + y² = 25.

Front

What is the radius of a circle with the equation (x + 2)² + (y - 3)² = 16?

Back

The radius is 4, since r² = 16.

Front

If a circle has a center at (1, -1) and a radius of 3, what is its equation?

Back

The equation is (x - 1)² + (y + 1)² = 9.

Front

What is the distance formula used for in relation to circles?

Back

The distance formula is used to find the distance between the center of the circle and any point on the circle, which equals the radius.

Front

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

Back

By substituting the point's coordinates into the circle's equation and comparing the result to r².

Front

What is the significance of the radius in a circle?

Back

The radius is the distance from the center to any point on the circle, defining its size.

Front

Write the equation of a circle with center (-3, 2) and radius 1.

Back

The equation is (x + 3)² + (y - 2)² = 1.