EOC Review Circle Equations

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 standard form (x - h)² + (y - k)² = r², identify the values of h and 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, thus r = √16 = 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 are the coordinates of the center and radius of the circle given by the equation x² + y² - 6x + 8y - 24 = 0?

Back

Center (3, -4) and radius 5 units.

Front

What does the term 'completing the square' mean in the context of circle equations?

Back

Completing the square involves rewriting a quadratic expression in the form (x - p)² + (y - q)² = r² to identify the center and radius.

Front

Given the center (1, 2) and radius 3, write the equation of the circle.

Back

The equation is (x - 1)² + (y - 2)² = 9.

Front

What is the distance formula used for in relation to circles?

Back

The distance formula is used to find the radius by calculating the distance between the center and a point on 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, it's inside; if equal, it's on; if greater, it's outside.

Front

What is the significance of the radius in the equation of a circle?

Back

The radius determines the size of the circle and is the distance from the center to any point on the circle.