Intersection of a Circle and a Line Quiz

The video tutorial explains how to find the intersection points between a circle and a line algebraically. It covers the possibilities of intersection, solving the linear equation for a variable, substituting to form a quadratic equation, factoring the quadratic to find solutions, and finally calculating the intersection points. The process involves solving for variables, substitution, and factoring to determine the points where the circle and line intersect.

What are the possible outcomes when a line intersects a circle?

• Two points, three points, or four points

• No intersection, one point, or three points

• One point, two points, or three points

• No intersection, one point, or two points

What is the first step in solving the intersection of a circle and a line?

• Solve the quadratic equation

• Graph the circle and line

• Solve the linear equation for one variable

• Find the radius of the circle

After solving the linear equation, what is the next step?

• Substitute the value into the circle's equation

• Graph the solutions

• Solve for the radius

• Check for extraneous solutions

What type of equation is formed after substituting the linear solution into the circle's equation?

• Cubic equation

• Exponential equation

• Quadratic equation

• Linear equation

What is the purpose of factoring the quadratic equation in this context?

• To simplify the linear equation

• To find the radius of the circle

• To determine the slope of the line

• To find the y-values of the intersection points

What do you do after finding the solutions to the quadratic equation?

• Graph the solutions

• Check for extraneous solutions

• Solve for the radius

• Substitute them back into the linear equation

If the quadratic equation solutions are y-values, what should you do next?

• Substitute them into the linear equation

• Solve for the radius

• Substitute them into the circle's equation

• Graph the solutions

What are the coordinates of the intersection points found in the example?

• (-3, -5) and (5, 3)

• (3, 5) and (-5, -3)

• (-5, 3) and (3, -5)

• (5, -3) and (-3, 5)