Practice Test - Writing Equations of Circles & Lines

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 of a circle from its equation?

Back

To find the radius from the equation (x - h)² + (y - k)² = r², take the square root of r².

Front

What is the slope-intercept form of a line?

Back

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

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the equation of a line with slope 3/4 passing through the point (4, -2)?

Back

The equation is y = (3/4)x - 5.

Front

What is the formula to convert a quadratic equation to standard form?

Back

To convert to standard form, complete the square for the quadratic terms.

Front

What does the term 'standard form' mean in the context of a circle's equation?

Back

Standard form means the equation is expressed as (x - h)² + (y - k)² = r².

Front

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

Back

The center (h, k) can be found from the equation (x - h)² + (y - k)² = r².

Front

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

Back

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

Front

How do you determine if a point lies on a line given by an equation?

Back

Substitute the x-value of the point into the equation and check if the resulting y-value matches the point's y-value.