Circle Geometry Concepts

The video tutorial explains how to write the centered equation of a circle given the endpoints of its diameter. It covers finding the center using the midpoint formula and calculating the radius using the distance formula. Finally, it demonstrates how to write the standard equation of the circle using the derived values.

What are the coordinates of the endpoints of the diameter of the circle?

• (1,1) and (3,3)

• (0,0) and (2,2)

• (-1,0) and (5,4)

• (-2,1) and (4,3)

What is the formula used to find the midpoint of a line segment?

• (x1 / x2), (y1 / y2)

• (x1 * x2)/2, (y1 * y2)/2

• (x1 - x2)/2, (y1 - y2)/2

• (x1 + x2)/2, (y1 + y2)/2

What are the coordinates of the center of the circle?

• (0,0)

• (1,2)

• (2,1)

• (3,4)

What is the significance of the midpoint in the context of a circle's diameter?

• It is the radius of the circle

• It is the endpoint of the diameter

• It is the circumference of the circle

• It is the center of the circle

Which formula is used to calculate the distance between two points?

• Distance = √((x2 - x1)² + (y2 - y1)²)

• Distance = (x2 - x1) + (y2 - y1)

• Distance = (x2 * x1) + (y2 * y1)

• Distance = (x2 + x1)² + (y2 + y1)²

What is the length of the radius of the circle?

• 10

• √5

• 5

• √10

What is the value of R squared in the standard equation of the circle?

• 10

• 20

• 5

• √10

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

• (x + h) + (y + k) = r

• (x - h) + (y - k) = r

• (x + h)² + (y + k)² = r²

• (x - h)² + (y - k)² = r²

What is the equation of the circle with center (1,2) and radius √10?

• (x - 1)² + (y - 2)² = 10

• (x + 1)² + (y + 2)² = √10

• (x + 1)² + (y + 2)² = 10

• (x - 1)² + (y - 2)² = √10

Why do we square the radius in the standard equation of a circle?

• To match the format of the equation

• To simplify calculations

• To find the diameter

• To find the circumference