Equation of a Circle Centered at a Point: Explained and Solved Examples

The video tutorial explains the equations of circles centered at a specific point (a,b) and at the origin (0,0). It covers the general formula for these equations, relates them to Pythagoras' theorem, and provides examples of calculating the equation of a circle given its center and a point on its circumference. The tutorial also discusses translating circles from the origin to another point and expanding the equations into different forms.

What is the general formula for the equation of a circle centered at the origin?

• x^2 + y^2 = 2r

• x^2 - y^2 = r^2

• x^2 + y^2 = r^2

• x + y = r^2

How do you calculate the horizontal length from the center to a point on the circle?

• b - y

• a - x

• x - a

• y - b

If a circle is centered at (3, 2) and passes through (6, 6), what is the radius?

• 3

• 6

• 5

• 4

What happens to a circle when it is translated from the origin to a new center point?

• It changes shape

• It moves to a new location

• It rotates

• It shrinks

How do you adjust the equation of a circle when translating it 3 units left and 4 units up?

• x - 3, y - 4

• x + 3, y + 4

• x + 3, y - 4

• x - 3, y + 4

What is the expanded form of (x + 3)^2?

• x^2 + 9

• x^2 + 3x

• x^2 + 6x + 9

• x^2 + 3x + 9

In the expanded equation x^2 + y^2 + 6x - 8y + 16 = 0, what is the coefficient of y?

• 16

• 6

• -8

• 0