Finding the Center and Radius of a Circle using Completing the Square

This video tutorial explains how to find the center and radius of a circle by converting its equation from general form to standard form using the method of completing the square. It reviews the process of completing the square, demonstrates how to apply it to circle equations, and highlights common mistakes to avoid, such as forgetting to balance the equation.

What is the main challenge in identifying the center and radius from the general form of a circle equation?

• The equation lacks variables.

• The equation is already in standard form.

• The equation is not in a recognizable format.

• The coefficients are too large.

What is the first step in completing the square for a quadratic equation?

• Multiply the equation by 2.

• Add a constant to both sides.

• Take half of the second coefficient and square it.

• Subtract the constant from both sides.

In the process of completing the square, what do you do after creating a perfect square trinomial?

• Factor it into a perfect square.

• Subtract the trinomial from both sides.

• Add the trinomial to both sides.

• Divide the equation by the trinomial.

What is the standard form of a circle's equation?

• x^2 + y^2 = r^2

• x - h + y - k = r

• x - h^2 + y - k^2 = r

• x - h^2 + y - k^2 = r^2

When converting a circle equation to standard form, what do the h and k values represent?

• The radius of the circle

• The circumference of the circle

• The diameter of the circle

• The center of the circle

What is a common mistake when completing the square for circle equations?

• Ignoring the coefficients

• Multiplying the equation by zero

• Forgetting to factor the equation

• Not adding the same value to both sides

In the final example, what is the correct radius of the circle after balancing the equation?

• Square root of 36

• Square root of 47

• Square root of 4

• Square root of 7