🧩🎯Equation of a Circle Skill Check

Front

What is the standard form of the equation of a circle?

Back

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

Front

How do you identify the center and radius from the equation of a circle?

Back

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

Front

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

Back

The radius is half the length of the diameter. If the diameter is d, then the radius r = d/2.

Front

How do you convert the diameter of a circle to its radius?

Back

To convert the diameter to radius, divide the diameter by 2: r = d/2.

Front

What is the equation of a circle with center at the origin and radius r?

Back

The equation is x² + y² = r².

Front

How do you derive the equation of a circle given its center and radius?

Back

Use the standard form (x - h)² + (y - k)² = r², substituting the center (h, k) and radius r.

Front

What is the significance of the radius in the context of a circle?

Back

The radius determines the size of the circle and is the distance from the center to any point on the circle.

Front

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

Back

From the equation (x - h)² + (y - k)² = r², the center is found at the point (h, k).

Front

What does the term 'standard form' refer to in the context of a circle's equation?

Back

Standard form refers to the specific way of writing the equation of a circle that clearly shows the center and radius.

Front

If a circle has a center at (2, -3) and a radius of 4, what is its equation?

Back

The equation is (x - 2)² + (y + 3)² = 16.