Equations of Circles Formula

How can you identify the graph of a circle from its equation?

• By recognizing the standard form (x-h)² + (y-k)² = r² and locating the center (h, k) and radius r.

• By checking if the equation is linear and finding the slope.

• By determining if the equation has only one variable and solving for it.

• By identifying the equation as a polynomial of degree 2 without any restrictions.

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

• The area A of a circle is given by the formula A = πr², where r is the radius.

• The area A of a circle is given by the formula A = 2πr, where r is the radius.

• The area A of a circle is given by the formula A = πd², where d is the diameter.

• The area A of a circle is given by the formula A = r², where r is the radius.

How do you find the radius from the equation of a circle?

• By taking the square root of the number on the right side of the equation in standard form: (x-h)² + (y-k)² = r².

• By adding the values of h and k from the equation.

• By multiplying the coefficients of x and y in the equation.

• By finding the distance between the center and any point on the circle.

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

• It represents the diameter of the circle.

• It indicates the circumference of the circle.

• The number on the right side of the equation represents the square of the radius.

• It shows the area of the circle.

In the equation (x-4)² + (y+4)² = 25, what is the center of the circle?

• (4, -4)

• (4, 4)

• (-4, -4)

• (-4, 4)

How can you determine the center of the circle from the equation (x-3)² + (y-2)² = 16?

• (3, 2)

• (4, 3)

• (2, 4)

• (1, 1)

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

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

• x² + y² = r², where r is the radius and the center is at the origin.

• (x-h)² + (y-k)² = 2r, where (h, k) is the center and r is the radius.

• (x-h)² + (y-k)² = (r+1)², where (h, k) is the center and r is the radius.

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

• The radius of the circle

• The coordinates (h, k) in the equation

• The diameter of the circle

• The circumference of the circle

If the equation of a circle is given as (x+1)² + (y-5)² = 36, what is the center?

• (-1, 5)

• (1, -5)

• (0, 0)

• (5, -1)

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

• By factoring the equation into linear terms.

• By completing the square for both x and y terms.

• By using the quadratic formula to find the roots.

• By rearranging the equation to isolate y.