Equations of Circles

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 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 the x and y terms.

Front

What is the center of the circle in the equation (x + 3)² + (y - 2)² = 16?

Back

The center of the circle is (-3, 2).

Front

What is the radius of the circle in the equation (x - 1)² + (y + 4)² = 25?

Back

The radius of the circle is 5.

Front

If the center of a circle is at (0, 0) and the radius is 4, what is the equation of the circle?

Back

The equation of the circle is x² + y² = 16.

Front

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

Back

Completing the square involves rewriting a quadratic expression in the form (x - p)² + (y - q)² = r² to identify the center and radius.

Front

In the equation (x - 2)² + (y + 3)² = 9, what is the radius?

Back

The radius is 3.

Front

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

Back

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

Front

How do you find the radius if given the center and a point on the circle?

Back

Use the distance formula: r = √[(x2 - x1)² + (y2 - y1)²], where (x1, y1) is the center and (x2, y2) is the point on the circle.

Front

What is the general form of a circle's equation?

Back

The general form of a circle's equation is x² + y² + Dx + Ey + F = 0.