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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 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: (x - h)² + (y - k)² = r².

Front

What are the coordinates of the center of a circle given by the equation (x - 4)² + (y - 3)² = 25?

Back

The center of the circle is at the point (4, 3).

Front

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

Back

The radius is 4 units, since √16 = 4.

Front

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

Back

The equation is x² + y² = 9.

Front

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

Back

To convert, complete the square for the x and y terms in the equation Ax² + Ay² + Bx + Cy + D = 0.

Front

What is the center and radius of the circle given by the equation (x - 1)² + (y + 2)² = 9?

Back

Center: (1, -2), Radius: 3 units.

Front

What does the term 'completing the square' mean in relation to circles?

Back

Completing the square is a method used to rewrite a quadratic equation in standard form, making it easier to identify the center and radius of a circle.

Front

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

Back

It represents the square of the radius of the circle.

Front

If a circle's equation is given as (x + 3)² + (y - 4)² = 25, what are the center and radius?

Back

Center: (-3, 4), Radius: 5 units.