Finding the Equation of a Circle with Given Radius and Center

This video tutorial explains how to find the equation of a circle using the center-radius form. It covers three examples: calculating the equation with given center and radius, and deriving the equation from a graph. The standard form of a circle equation is introduced, and step-by-step solutions are provided for each example.

What is the standard form of a circle's equation?

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

• x^2 + y^2 + r^2 = 0

What does 'r' represent in the standard form of a circle's equation?

• The area of the circle

• The radius of the circle

• The circumference of the circle

• The diameter of the circle

If a circle's equation is (x - h)^2 + (y - k)^2 = r^2, what do 'h' and 'k' represent?

• The circle's center coordinates

• The coordinates of any point on the circle

• The slope of the tangent to the circle at any point

• The diameter's endpoints

What is the correct way to express a circle's radius in its equation?

• As the diameter divided by 2

• As the value 'r' squared on the right side of the equation

• As the square root of the right side of the equation

• As the square of the right side of the equation

Given a circle with center (15, 14) and radius 7, what is its equation?

• (x - 15)^2 + (y - 14)^2 = 49

• (x + 15)^2 + (y + 14)^2 = 49

• (x - 7)^2 + (y - 7)^2 = 196

• (x + 7)^2 + (y + 7)^2 = 49

How is the equation of a circle derived when given its center and radius?

• By calculating the distance between the center and any point on the circle

• By drawing the circle and measuring its diameter

• By substituting the center's coordinates and radius into the standard form

• By squaring the radius and adding it to the center's coordinates

For a circle centered at (0, -6) with a radius of 3, what is the correct equation?

• (x + 3)^2 + (y - 6)^2 = 9

• (x - 3)^2 + (y + 6)^2 = 0

• x^2 + (y - 6)^2 = 9

• x^2 + (y + 6)^2 = 9

How do you determine the center of a circle from its graph?

• By calculating the average of all points on the circle

• By identifying the opposite of the point to the 2x axis

• By locating the point where it crosses the x-axis

• By finding the midpoint of the diameter

What is the radius of a circle if its graph extends 5 units in all directions from its center?

• 20 units

• 10 units

• 5 units

• 2.5 units

Given a circle's center at (-1, -2) and a radius of 5, what is its equation?

• (x - 1)^2 + (y + 2)^2 = 25

• (x + 1)^2 + (y - 2)^2 = 25

• (x - 1)^2 + (y - 2)^2 = 25

• (x + 1)^2 + (y + 2)^2 = 25