Write the equation of a circle given center and tangent to the x axis

The video tutorial explains how a circle is tangent to the X axis, meaning it touches the axis at one point. It highlights the importance of knowing the circle's radius and center to define it. The tutorial then derives the equation of the circle using these properties, showing that the radius is 2 and the center is at (4, 2). The final equation is presented as (X - 4)^2 + (Y - 2)^2 = 4.

What does it mean for a circle to be tangent to the X-axis?

• It touches the X-axis at exactly one point.

• It is parallel to the X-axis.

• It crosses the X-axis at two points.

• It does not interact with the X-axis.

Why is knowing the radius and center of a circle important?

• They help in calculating the area of the circle.

• They are used to find the circumference.

• They determine the color of the circle.

• They are the only components needed to define a circle.

What is the center of the circle in the given example?

• (1, 1)

• (2, 4)

• (4, 2)

• (0, 0)

What is the radius of the circle in the example?

• 4

• 3

• 2

• 1

What is the equation of the circle as derived in the tutorial?

• (x - 2)^2 + (y - 4)^2 = 4

• (x - 4)^2 + (y - 2)^2 = 4

• (x + 4)^2 + (y + 2)^2 = 4

• (x + 2)^2 + (y + 4)^2 = 4