Graphing Circles

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

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

Front

What is the radius of a circle given the equation (x - 2)² + (y + 3)² = 16?

Back

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

Front

If the diameter of a circle is 10, what is the radius?

Back

The radius is 5 units, since the radius is half of the diameter.

Front

What are the coordinates of the center of the circle with equation (x + 1)² + (y - 4)² = 9?

Back

The center is (-1, 4).

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

Back

The equation is x² + y² = 9.

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, which helps identify the center and radius of a circle.

Front

What is the relationship between the radius and the area of a circle?

Back

The area A of a circle is given by A = πr², where r is the radius.

Front

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

Back

Substitute the point (x, y) into the circle's equation. If the result is less than r², it's inside; if equal, it's on; if greater, it's outside.