Intersection Points and Circle Equations

The video tutorial explains how to find the intersection point of the line y = 2x and a circle with radius 4 centered at the origin. It begins by deriving the equations of the circle and the line, then uses substitution to solve the system of equations. The tutorial demonstrates how to rationalize the coordinates and convert them to decimal approximations. Finally, it verifies the solution graphically, ensuring the intersection point is in the first quadrant.

What is the equation of the circle centered at the origin with a radius of 4?

• x^2 + y^2 = 4

• x^2 + y^2 = 8

• x^2 + y^2 = 12

• x^2 + y^2 = 16

Which equation represents the line that intersects the circle?

• y = x

• y = 3x

• y = 2x

• y = 4x

What method is used to solve the system of equations for the intersection point?

• Elimination

• Substitution

• Graphing

• Matrix method

What is the x-coordinate of the intersection point in the first quadrant?

• 8/sqrt(5)

• 6/sqrt(5)

• 2/sqrt(5)

• 4/sqrt(5)

How do you find the y-coordinate of the intersection point?

• Divide x by 2

• Add 2 to x

• Multiply x by 3

• Multiply x by 2

What is the y-coordinate of the intersection point in the first quadrant?

• 2/sqrt(5)

• 8/sqrt(5)

• 6/sqrt(5)

• 4/sqrt(5)

What is the rationalized form of the x-coordinate?

• 2 sqrt(5)/5

• 4 sqrt(5)/5

• 6 sqrt(5)/5

• 8 sqrt(5)/5

What is the decimal approximation of the x-coordinate rounded to three decimal places?

• 1.678

• 1.890

• 1.789

• 1.567

What is the decimal approximation of the y-coordinate rounded to three decimal places?

• 3.678

• 3.456

• 3.789

• 3.578

How does the graphical verification support the solution?

• The x-coordinate is more than 2

• The y-coordinate is less than 3.5

• The x-coordinate is less than 2 and the y-coordinate is more than 3.5

• Both coordinates are exactly 2 and 3.5