Circle Geometry Concepts

The video tutorial explains the equation of a circle, identifying its center and radius. It demonstrates how to find where the circle intersects the X and Y axes and verifies if specific points lie on the circle. Additionally, it covers calculating the midpoint between two points on the circle and the distance from the circle's center.

What is the center of the circle given by the equation (x - 3)^2 + (y - 2)^2 = 20?

• (-3, 2)

• (3, -2)

• (-3, -2)

• (3, 2)

What is the radius of the circle given by the equation (x - 3)^2 + (y - 2)^2 = 20?

• 4

• 5

• √20

• 10

What is the equation of a circle with center (h, k) and radius r?

• (x + h)^2 - (y + k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• (x - h)^2 - (y - k)^2 = r^2

If a circle has a radius of 5, what is the area of the circle?

• 25π

• 10π

• 5π

• 50π

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

• x^2 + y^2 + 2x + 2y = 0

• x^2 + y^2 = r^2

• x^2 + y^2 + Dx + Ey + F = 0

• (x - h)^2 + (y - k)^2 = r^2

What is the length of the radius if the circle's equation is (x - 3)^2 + (y - 2)^2 = 25?

• √25

• 10

• 25

• 5

Where does the circle intersect the x-axis?

• (3, 0) and (-3, 0)

• (0, 3) and (0, -3)

• (0, 7) and (0, -1)

• (7, 0) and (-1, 0)

What is the x-coordinate of the point where the circle intersects the x-axis?

• 0 and 0

• 5 and -5

• 3 and -3

• 7 and -1

What is the value of y when the circle intersects the y-axis?

• √20 and -√20

• 5 and -5

• √11 + 2 and -√11 + 2

• √11 - 2 and -√11 - 2

What is the y-coordinate of the point where the circle intersects the y-axis?

• √11 + 2 and -√11 + 2

• 3 and -3

• 5 and -5

• 0 and 0