Circle Geometry and Equations

This video tutorial covers the equations of circles, including how to find the center and radius from given equations, write circle equations, and calculate midpoints and diameters. It also explores the relationship between area and radius, and how to find tangent equations. The tutorial provides step-by-step solutions to various problems, enhancing understanding of circle geometry.

What is the center of a circle with the equation x² + y² = 16?

• (4, 4)

• (0, 0)

• (0, 16)

• (16, 0)

If the equation of a circle is (x - 3)² + (y + 2)² = 5, what is the radius?

• 3

• √5

• 5

• 2

How do you find the center of a circle given the equation (x + 3)² + (y - 1)² = 10?

• (3, -1)

• (-3, 1)

• (1, -3)

• (-1, 3)

What is the equation of a circle with center (0, 6) and radius 0.5?

• x² + (y - 6)² = 0.25

• x² + (y + 6)² = 0.5

• (x - 6)² + y² = 0.25

• (x + 6)² + y² = 0.5

Given a circle with center (1, 3) and a point (9, 9) on the circle, what is the radius?

• 4

• 6

• 10

• 8

How do you find the midpoint of a line segment with endpoints (-5, 1) and (5, 23)?

• (0, 11)

• (-5, 12)

• (5, 12)

• (0, 23)

What is the equation of a circle with center (0, 11) and radius 13?

• x² + y² = 169

• (x - 11)² + y² = 169

• (x + 11)² + y² = 169

• x² + (y - 11)² = 169

If two circles have the same center and the first has a radius of 10, what is the area of the second circle if its radius is 14?

• 196π

• 100π

• 4π

• 96π

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

• (x - 1)² + (y + 2)² = 4

• (x + 1)² + (y - 2)² = 4

• (x - 1)² + (y - 2)² = 4

• (x + 1)² + (y + 2)² = 4

How do you find the equation of a tangent to a circle at a point?

• Use the same gradient as the radius

• Use the radius's gradient directly

• Find the negative reciprocal of the radius's gradient

• Double the radius's gradient