A2H HW #29: Section 5.2

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

To find the radius of a circle from its equation in standard form (x - h)² + (y - k)² = r², take the square root of r².

Front

What is the center of the circle in the equation (x + 2)² + (y - 3)² = 4?

Back

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

Front

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

Back

The radius of the circle is 2.

Front

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

Back

The standard equation is x² + y² = 16.

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 x and y.

Front

What is the center-radius form of a circle?

Back

The center-radius form of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

Determine the center and radius from the equation (x + 2)² + (y + 3)² = 49.

Back

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

Front

What is a solution to the system of equations x² + y² = 41 and y = 3x - 7?

Back

One solution is (4, 5).

Front

How do you solve a system of linear and quadratic equations?

Back

Substitute the linear equation into the quadratic equation and solve for the variable.