Equations of Circles (CTS)

Front

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

Back

The standard form 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 radius of a circle from its equation?

Back

The radius can be found by taking the square root of the number on the right side of the equation in standard form.

Front

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

Back

The center (h,k) represents the point in the Cartesian plane around which the circle is drawn.

Front

Convert the equation x² + y² = 25 to standard form.

Back

The standard form is (x-0)² + (y-0)² = 25.

Front

What is the radius of the circle given by the equation (x-3)² + (y+4)² = 16?

Back

The radius is 4, since r² = 16.

Front

Identify the center of the circle from the equation (x+1)² + (y-2)² = 36.

Back

The center is (-1, 2).

Front

What is the equation of a circle with center (0,0) and radius 5?

Back

The equation is x² + y² = 25.

Front

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

Back

Complete the square for both x and y terms.

Front

What is the center and radius of the circle given by the equation x² + y² - 6x + 8y = 0?

Back

Center is (3, -4) and radius is 5.

Front

What does the term 'completing the square' mean in the context of circles?

Back

It is a method used to rewrite a quadratic equation in standard form.