Write the Equation of a Circle Given Parts Easy Medium Hard

This video tutorial explains how to write the equation of a circle using different pieces of information. It covers the standard forms of circle equations, including those centered at the origin and those with transformations. Through examples, the video demonstrates how to use given center and radius, solve for R-squared with a point on the circle, and find the center and radius from diameter endpoints.

What is the equation of a circle centered at the origin?

• (x + h)^2 + (y + k)^2 = r^2

• x^2 + y^2 = 2r

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = r^2

If a point (x, y) lies on a circle with center (h, k), what is the unknown variable needed to write the circle's equation?

• The diameter

• The y-coordinate of the center

• The radius

• The x-coordinate of the center

When substituting values into the circle equation, why is it important to use parentheses?

• To avoid errors with negative values

• To make the equation look neat

• To ensure the equation is balanced

• To simplify the equation

How can you find the center of a circle if you are given the endpoints of its diameter?

• By multiplying the x-coordinates and y-coordinates

• By finding the average of the x-coordinates and y-coordinates

• By dividing the x-coordinates and y-coordinates

• By subtracting the x-coordinates and y-coordinates

What does the diameter of a circle represent?

• The distance across the circle through the center

• The distance from the center to any point on the circle

• The circumference of the circle

• The area of the circle

What is the formula to find the midpoint of two points (x1, y1) and (x2, y2)?

• ((x1 / x2)/2, (y1 / y2)/2)

• ((x1 + x2)/2, (y1 + y2)/2)

• ((x1 - x2)/2, (y1 - y2)/2)

• ((x1 * x2)/2, (y1 * y2)/2)

What is the relationship between the radius and the diameter of a circle?

• The radius is equal to the diameter

• The radius is unrelated to the diameter

• The radius is half the diameter

• The radius is twice the diameter