Equations of a Cirlce

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 and r is the radius.

Front

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

Back

The center of a circle can be found from the equation (x - h)² + (y - k)² = r² by identifying the values of h and k.

Front

What is the radius of a circle?

Back

The radius of a circle is the distance from the center to any point on the circle, represented by r in the equation.

Front

If the equation of a circle is (x + 2)² + (y - 5)² = 16, what is the center?

Back

The center of the circle is (-2, 5).

Front

What is the diameter of a circle?

Back

The diameter of a circle is twice the radius, represented as d = 2r.

Front

How do you calculate the diameter from the equation of a circle?

Back

The diameter can be calculated as d = 2√r², where r is the radius from the equation.

Front

What does the term 'h' represent in the circle equation?

Back

In the equation (x - h)² + (y - k)² = r², 'h' represents the x-coordinate of the center of the circle.

Front

What does the term 'k' represent in the circle equation?

Back

In the equation (x - h)² + (y - k)² = r², 'k' represents the y-coordinate of the center of the circle.

Front

Write the equation of a circle with center (0, 0) and radius 4.

Back

The equation is x² + y² = 16.

Front

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

Back

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