QZ-MA: Circles--Equations & Graphing

Front

What is the standard equation of a circle?

Back

The standard equation of a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r².

Front

How do you find the center of a circle from its equation?

Back

To find the center of a circle from its equation in standard form (x - h)² + (y - k)² = r², identify the values of h and k.

Front

What is the radius of a circle?

Back

The radius of a circle is the distance from the center to any point on the circle. In the equation (x - h)² + (y - k)² = r², r is the radius.

Front

Given the equation (x + 2)² + (y - 3)² = 16, what is the center and radius?

Back

Center: (-2, 3), Radius: 4.

Front

What does the term 'diameter' refer to in a circle?

Back

The diameter of a circle is twice the length of the radius and is the longest distance across the circle.

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 relationship between the radius and diameter of a circle?

Back

The diameter is twice the radius: Diameter = 2 * Radius.

Front

If the center of a circle is at (0, 0) and the radius is 5, what is the equation of the circle?

Back

The equation is x² + y² = 25.

Front

What is the significance of the values h and k in the circle's equation?

Back

In the equation (x - h)² + (y - k)² = r², h and k represent the x and y coordinates of the center of the circle.

Front

How do you determine if a point lies inside, on, or outside a circle?

Back

Calculate the distance from the point to the center. If it's less than the radius, the point is inside; if equal, on; if greater, outside.