9.3 Flashcard - Equation of Circles

Front

What is the standard equation of a circle?

Back

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

Front

Back

Center: (12, -6), Radius: 4.

Front

Back

Center: (28, -23), Radius: 25.

Front

What does the variable 'r' represent in the standard equation of a circle?

Back

The variable 'r' represents the radius of the circle.

Front

What does the variable '(h, k)' represent in the standard equation of a circle?

Back

The variable '(h, k)' represents the coordinates of the center of the circle.

Front

Write the standard equation of a circle with center (8, 14) and radius 10.

Back

Front

Back

The radius is 7, since r² = 49.

Front

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

Back

Front

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

Back

To find the center, rewrite the equation in the form (x - h)² + (y - k)² = r² and identify (h, k).

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.