Deriving the Equation of a Circle Using the Pythagorean Theorem

This video tutorial explains how to derive the equation of a circle centered at the origin using the Pythagorean theorem. It begins with a review of the Pythagorean theorem and its application to right triangles. The tutorial then defines a circle and its properties, such as the center and radius. By applying the Pythagorean theorem, the video derives the equation x^2 + y^2 = r^2 for a circle centered at the origin. Examples are provided to illustrate how to find the equation of specific circles and determine if points lie on them.

What mathematical theorem is used to derive the equation of a circle centered at the origin?

• Binomial Theorem

• Fermat's Last Theorem

• Pythagorean Theorem

• Fundamental Theorem of Calculus

What is the term for the distance from the center of a circle to any point on the circle?

• Chord

• Radius

• Circumference

• Diameter

Which equation represents a circle centered at the origin with radius r?

• x^2 + y^2 = r^2

• x + y = r

• x^2 + y = r

• x^2 - y^2 = r^2

If a circle is centered at the origin and passes through the point (6, 8), what is the radius of the circle?

• 8

• 10

• 6

• 12

How do you determine if a point lies on a given circle?

• Check if the point satisfies the circle's equation

• Find the midpoint between the point and the center

• Calculate the slope of the line through the point and the center

• Measure the distance from the point to the center

What is the equation of a circle with a radius of 8 centered at the origin?

• x^2 + y^2 = 64

• x^2 + y^2 = 16

• x^2 + y^2 = 32

• x^2 + y^2 = 8

What is the first step in finding the equation of a circle that passes through a specific point?

• Determine the circumference of the circle

• Calculate the slope of the line through the point

• Draw a right triangle using the point

• Find the midpoint of the line segment from the origin to the point