Convert polar equation to rectangular by completing the square

The video tutorial explains how to manipulate an equation involving R and Theta by multiplying both sides by R, leading to a form that allows completing the square. This process reveals a circle with a radius of two, shifted two units to the right. The tutorial concludes with a recap of the steps and encourages students to verify the results using a calculator.

What is the first step in converting the polar equation R = 4 cos(Theta) into a Cartesian form?

• Divide by R on both sides

• Multiply by R on both sides

• Add R to both sides

• Subtract R from both sides

When completing the square for the equation X^2 - 4X + Y^2 = 0, what value is added to both sides?

• 16

• 8

• 4

• 2

What is the resulting equation after completing the square for X^2 - 4X + Y^2?

• (X - 2)^2 + Y^2 = 4

• (X + 2)^2 + Y^2 = 4

• (X - 2)^2 + Y^2 = 0

• (X + 2)^2 + Y^2 = 0

What geometric shape does the equation (X - 2)^2 + Y^2 = 4 represent?

• Circle

• Parabola

• Ellipse

• Hyperbola

How is the circle described by the equation (X - 2)^2 + Y^2 = 4 positioned in the coordinate plane?

• Shifted 2 units to the left with radius 2

• Centered at the origin with radius 4

• Shifted 2 units to the right with radius 2

• Centered at the origin with radius 2