Finding the Standard Equation of a Circle

The video tutorial explains how to write the standard equation of a circle given its center and a point on the circle. It covers the use of the distance formula to find the radius and demonstrates how to simplify the equation. The final standard equation is derived, and the approximate decimal value of the radius is provided for graphing purposes.

What is the standard equation of a circle?

• x^2 + y^2 = 2r

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = r^2

• (x + h)^2 + (y + k)^2 = r

What are the coordinates of the center of the circle?

• (2, -2)

• (4, -1)

• (1, -4)

• (-1, 4)

What does 'h' and 'k' represent in the circle's equation?

• Radius and diameter

• X and Y coordinates of the center

• Diameter and circumference

• X and Y intercepts

How is the radius of the circle determined?

• Using the midpoint formula

• By doubling the distance from the center to a point

• By squaring the center's coordinates

• Through the distance formula between two points

What formula is used to find the distance between two points?

• Midpoint formula

• Slope formula

• Distance formula

• Perimeter formula

What is the value of R squared in the equation?

• 9

• 36

• 3√5

• 45

What is the simplified form of the radius?

• 6.71

• 9

• 3√5

• √45

How do you transform x - -1 in the equation?

• -x + 1

• x + 1

• x - 1

• -x - 1

What is the approximate decimal value of the radius?

• 9

• 45

• 6.71

• 3

What is the purpose of finding the radius in decimal form?

• To simplify the equation

• For easier graphing on the coordinate plane

• To calculate the area of the circle

• To determine the circumference