Completing the Square and Circle Equations

The video tutorial explains how to find the center and radius of a circle given its equation. The process involves rewriting the equation to eliminate coefficients of x² and y², completing the square for both x and y terms, and then finalizing the equation to identify the center coordinates and radius. The tutorial provides a step-by-step approach to solving the problem, ensuring clarity in each stage of the process.

What is the initial equation of the circle given in the problem?

• 2x^2 + 2y^2 - 5x + 8y + 10 = 0

• x^2 + y^2 + 5x - 8y + 10 = 0

• 2x^2 + 2y^2 + 5x - 8y + 10 = 0

• x^2 + y^2 - 5x + 8y + 10 = 0

What is the first step in simplifying the circle equation?

• Add 5 to both sides

• Subtract 10 from both sides

• Multiply the entire equation by 2

• Divide the entire equation by 2

After dividing by 2, what is the coefficient of x in the simplified equation?

• 1

• 2

• 5/2

• 5

What mathematical technique is used to eliminate linear terms in the equation?

• Integration

• Factoring

• Completing the square

• Differentiation

What is the value added and subtracted when completing the square for the x terms?

• 5/4

• 5/2

• 5/8

• 5/16

What is the new form of the x terms after completing the square?

• (x - 5/2)^2

• (x - 5/4)^2

• (x + 5/4)^2

• (x + 5/2)^2

What is the value added and subtracted when completing the square for the y terms?

• 4^2

• 2^2

• 4

• 2

What is the new form of the y terms after completing the square?

• (y - 2)^2

• (y + 4)^2

• (y + 2)^2

• (y - 4)^2

What is the final form of the equation on the left-hand side?

• (x + 5/2)^2 + (y - 2)^2

• (x - 5/2)^2 + (y + 2)^2

• (x + 5/4)^2 + (y - 2)^2

• (x - 5/4)^2 + (y + 2)^2

What is the value of the radius squared in the final equation?

• 9/16

• 3/4

• 4/3

• 16/9