Understanding the Equation of a Circle

This video tutorial covers the equation of a circle, starting with the basic form x² + y² = r², where the center is at the origin. It explains how the equation changes when the circle's center is moved to a different point, using examples to illustrate the process. The tutorial also demonstrates how to draw circles from given equations and solve exam-style questions involving circle equations. Additionally, it covers finding the equation of a circle using the diameter's endpoints and deriving the equation of a tangent to a circle at a given point. The video concludes with a call to action for viewers to practice with exam questions.

What is the equation of a circle with a center at the origin and radius 5?

• x^2 + y^2 = 25

• x^2 + y^2 = 10

• x^2 + y^2 = 50

• x^2 + y^2 = 5

If a circle has a center at (3, -4) and a radius of 6, what is its equation?

• (x - 3)^2 + (y - 4)^2 = 36

• (x + 3)^2 + (y + 4)^2 = 36

• (x - 3)^2 + (y + 4)^2 = 36

• (x + 3)^2 + (y - 4)^2 = 36

How do you find the center of a circle from the equation (x - 2)^2 + (y + 3)^2 = 16?

• Center is at (-2, -3)

• Center is at (2, 3)

• Center is at (-2, 3)

• Center is at (2, -3)

Given a circle with center (1, -3) and a point (7, -11) on the circle, what is the radius?

• 12

• 10

• 14

• 8

If the diameter of a circle is defined by points (0, -10) and (14, 38), what is the center of the circle?

• (7, 14)

• (7, 24)

• (14, 7)

• (0, 0)

What is the radius of a circle with a diameter defined by points (0, -10) and (14, 38)?

• 25

• 12.5

• 20

• 15

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

• Use the gradient of the radius and a point on the tangent

• Use the circle's circumference

• Use the circle's radius and center

• Use the circle's diameter

What is the gradient of a tangent to a circle if the radius has a gradient of 3?

• -1/3

• 1/3

• -3

• 3

If a circle's equation is (x + 2)^2 + (y - 5)^2 = 49, what is the radius?

• 9

• 7

• 5

• 11

What is the equation of a tangent line to a circle at point (4, 11) if the gradient is -1/3?

• y = -1/3x + 37/3

• y = 1/3x + 37/3

• y = -1/3x - 37/3

• y = 1/3x - 37/3