Find the equation of a circle given the center and line tangent to the circle

The video tutorial explains how to write the equation of a circle given its center and the fact that it is tangent to the X axis. It covers the standard form of a circle's equation, the concept of tangency, and how to determine the radius by understanding the distance from the center to the X axis. The tutorial uses a step-by-step approach to ensure comprehension of these geometric concepts.

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

• (X + H)^2 + (Y + K)^2 = R^2

• (X - H)^2 + (Y - K)^2 = R^2

• X^2 + Y^2 = R^2

• X^2 + Y^2 = 2R

If a circle is tangent to the X-axis, how many points does it touch the axis?

• Two points

• No points

• One point

• Three points

What does it mean for a line to be tangent to a circle?

• It crosses the circle at two points

• It does not touch the circle

• It is parallel to the circle

• It touches the circle at exactly one point

How is the radius of the circle determined when it is tangent to the X-axis?

• By measuring the diameter of the circle

• By measuring the distance from the center to the X-axis

• By measuring the distance from the center to the Y-axis

• By measuring the circumference of the circle

What is the final equation of the circle given the center (-6, 5) and tangent to the X-axis?

• (X + 6)^2 + (Y - 5)^2 = 36

• (X - 6)^2 + (Y + 5)^2 = 36

• (X + 6)^2 + (Y + 5)^2 = 36

• (X - 6)^2 + (Y - 5)^2 = 36