Equation of the Circle

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 center of a circle from its equation?

Back

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

Front

What does the radius of a circle represent in its equation?

Back

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

Front

What is the center of the circle given by the equation (x - 3)² + (y + 4)² = 121?

Back

The center of the circle is (3, -4).

Front

What is the radius of the circle defined by the equation (x + 2)² + (y - 1)² = 16?

Back

The radius of the circle is 4, since r² = 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 equation of a circle with center at (0, 0) and radius 5?

Back

The equation is x² + y² = 25.

Front

What does the term (x - h)² represent in the equation of a circle?

Back

The term (x - h)² represents the horizontal distance squared from the center of the circle to a point on the circle.

Front

What is the significance of the value on the right side of the equation in (x - h)² + (y - k)² = r²?

Back

The value on the right side (r²) indicates the square of the radius of the circle.

Front

How can 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; equal to r², it's on; greater than r², it's outside.