Equation Of a Circle

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 find the center of a circle from its equation?

Back

To find the center of a circle from its equation in standard form (x - h)² + (y - k)² = r², identify the values of h and k. The center is (h, k).

Front

What is the radius of a circle in the equation (x - 4)² + (y - 1)² = 49?

Back

The radius is 7, since r² = 49, and r = √49 = 7.

Front

How do you determine the radius of a circle given its center and a point on the circle?

Back

Use the distance formula to find the distance between the center and the point on the circle. This distance is the radius.

Front

What is the equation of a circle with center (0, 0) and radius 3?

Back

The equation is x² + y² = 9.

Front

If a circle has a center at (2, -3) and a radius of 5, what is its equation?

Back

The equation is (x - 2)² + (y + 3)² = 25.

Front

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

Back

Standard form refers to the specific format (x - h)² + (y - k)² = r² that clearly indicates the center and radius of the circle.

Front

How can 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 both x and y terms.

Front

What is the center of the circle represented by the equation (x + 1)² + (y - 4)² = 16?

Back

The center is (-1, 4).

Front

What is the significance of the number on the right side of the equation in a circle's equation?

Back

The number on the right side (r²) represents the square of the radius of the circle.