Circle and Line Intersections

What does 'r' represent in the standard equation of a circle, x² + y² = r²?

• Radius

• Diameter

• Circumference

• Area

What is the maximum number of intersection points possible when a circle and a line intersect?

• Zero

• One

• Two

• Three

Given the system of equations: x² + y² = 20 and y = x + 2. What is the resulting equation after substituting the linear equation into the circle equation?

• x² + (x + 2)² = 20

• x² + y² = x + 2

• (x + 2)² + y² = 20

• x² + x² + 2² = 20

After simplifying the equation from the first example to x² + 2x - 8 = 0, what are the values of x?

• x = -4, x = 2

• x = 4, x = -2

• x = -8, x = 1

• x = 8, x = -1

What are the solution points (x, y) for the system x² + y² = 20 and y = x + 2?

• (-4, -2) and (2, 4)

• (-2, -4) and (4, 2)

• (-4, 2) and (2, -4)

• (4, -2) and (-2, 4)

After simplifying the equation from the second example to x² - 6x + 9 = 0, what is the value of x?

• x = -3

• x = 3

• x = 9

• x = -9

What is the solution point (x, y) for the system x² + y² = 10 and y = -3x + 10?

• (3, 1)

• (1, 3)

• (-3, 19)

• (3, -1)

When solving a system of equations involving a circle and a line, what indicates that there are no real solutions?

• The resulting quadratic equation has a positive discriminant.

• The resulting quadratic equation has a negative discriminant.

• The line is tangent to the circle.

• The line passes through the center of the circle.