Math 3 EOC Review

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 center of a circle from its equation?

Back

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

Front

What is the radius of a circle given the equation x² + (y + 6)² = 196?

Back

The radius is 14, since r² = 196, thus r = √196 = 14.

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 solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (2, 5).

Front

What does it mean for two lines to be parallel in a coordinate plane?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the distance formula between two points (x1, y1) and (x2, y2)?

Back

The distance d is given by d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the midpoint formula for two points (x1, y1) and (x2, y2)?

Back

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2).