Equation of a Circle part 1

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 with the equation (x + 3)² + (y - 2)² = 16?

Back

The radius is 4, since r² = 16, thus r = √16 = 4.

Front

What is the diameter of a circle?

Back

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

Front

Given the equation (x - 1)² + (y + 4)² = 25, what is the center?

Back

The center is (1, -4).

Front

What is the radius of a circle with the equation x² + y² = 36?

Back

The radius is 6, since r² = 36, thus r = √36 = 6.

Front

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

Back

To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for x and y.

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 - h)² to identify the center and radius of the circle.

Front

What is the center and radius of the circle given by the equation (x - 2)² + (y + 3)² = 49?

Back

The center is (2, -3) and the radius is 7.

Front

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

Back

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