Understanding Circle Equations

This video tutorial explains how to find the center and radius of a circle given its equation in standard form. It covers the identification of h and k values for the center and the calculation of the radius from r squared. The tutorial includes examples and an advanced problem using the completing the square method to convert equations into standard form.

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

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 + 2hx + 2ky = r^2

• x - h + y - k = r

If the equation of a circle is (x - 3)^2 + (y - 4)^2 = 25, what is the radius?

• 5

• 6

• 3

• 4

In the equation (x + 2)^2 + (y - 5)^2 = 49, what are the coordinates of the center?

• (2, 5)

• (-2, 5)

• (2, -5)

• (-2, -5)

What is the radius of a circle with the equation (x + 2)^2 + (y - 5)^2 = 49?

• 8

• 7

• 6

• 5

What should you do if a circle's equation is not in standard form?

• Integrate the equation

• Differentiate the equation

• Complete the square

• Use the quadratic formula

When completing the square, what is the first step?

• Multiply both sides by 2

• Take half of the coefficient of x or y and square it

• Factor the equation

• Add the same number to both sides

In the process of completing the square, what do you do after finding half of the coefficient and squaring it?

• Divide it by the radius

• Subtract it from both sides

• Add it to both sides

• Multiply it by the radius

What is a perfect square trinomial?

• A trinomial with three different terms

• A trinomial that can be factored into two identical binomials

• A trinomial with a constant term of zero

• A trinomial that cannot be factored

After completing the square, what is the next step to find the center of the circle?

• Graph the equation

• Solve for x and y

• Identify the values of h and k

• Calculate the radius

What is the radius of a circle if the equation is (x - 4)^2 + (y + 3)^2 = 36?

• 6

• 4

• 7

• 5