Circle Equations

Front

What is the standard form of a circle's equation?

Back

The standard form of a circle's equation 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 from the equation of a circle?

Back

The radius can be found by taking the square root of the number on the right side of the equation in standard form (x - h)² + (y - k)² = r².

Front

What is the center of the circle given by the equation (x - 4)² + (y + 2)² = 16?

Back

The center of the circle is (4, -2).

Front

Convert the equation x² + y² - 4x + 6y - 12 = 0 to standard form.

Back

The standard form is (x - 2)² + (y + 3)² = 1.

Front

What does the term 'h' represent in the standard form of a circle's equation?

Back

The term 'h' represents the x-coordinate of the center of the circle.

Front

What does the term 'k' represent in the standard form of a circle's equation?

Back

The term 'k' represents the y-coordinate of the center of the circle.

Front

If the radius of a circle is 7, what is the equation in standard form?

Back

The equation is (x - h)² + (y - k)² = 49, where (h, k) is the center.

Front

What is the equation of a circle with center (0, 0) and radius 5?

Back

The equation is x² + y² = 25.

Front

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

Back

Substitute the point's coordinates 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.

Front

What is the general form of a circle's equation?

Back

The general form is x² + y² + Dx + Ey + F = 0.