Circle Geometry Concepts

This lesson covers the equations of circles, both centered and not centered at the origin. It explains the relationship between any point on the circle and its radius, using the Pythagorean theorem. The lesson includes practice problems for writing circle equations and determining the position of a point relative to a circle. It also covers calculating the shortest distance from a point to a circle.

What is the definition of a circle?

• A line segment with two endpoints

• A shape with four equal sides

• A set of points equidistant from a center point

• A polygon with three sides

What is the radius of a circle?

• The circumference of the circle

• The diameter of the circle

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

• The area of the circle

How is the equation of a circle not centered at the origin expressed?

• x^2 - y^2 = r^2

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

What happens to the circle equation if the circle is centered at the origin?

• It becomes (x - h)^2 + (y - k)^2 = r^2

• It becomes x^2 - y^2 = r^2

• It becomes (x + h)^2 + (y + k)^2 = r^2

• It simplifies to x^2 + y^2 = r^2

Why does the equation x^2 + y^2 = r^2 describe a circle centered at the origin?

• Because it represents a rectangle

• Because it represents a triangle

• Because it represents the Pythagorean theorem in a right triangle

• Because it represents a square

What is the equation of a circle with center (0,0) and radius 3?

• x^2 + y^2 = 6

• x^2 + y^2 = 9

• x^2 + y^2 = 3

• x^2 + y^2 = 12

How do you find the radius from the equation x^2 + y^2 = 36?

• By taking the square root of 36

• By doubling 36

• By halving 36

• By subtracting 36 from 100

If a circle passes through the point (5,3) and is centered at the origin, what is the equation?

• x^2 + y^2 = 9

• x^2 + y^2 = 34

• x^2 + y^2 = 16

• x^2 + y^2 = 25

How can you determine if a point is inside a circle?

• If x^2 + y^2 is greater than the radius squared

• If x^2 + y^2 is not equal to the radius squared

• If x^2 + y^2 is less than the radius squared

• If x^2 + y^2 equals the radius squared

What is the equation of a circle with center (3,4) and radius 8?

• (x + 3)^2 + (y + 4)^2 = 64

• (x + 3)^2 + (y + 4)^2 = 8

• (x - 3)^2 + (y - 4)^2 = 8

• (x - 3)^2 + (y - 4)^2 = 64