Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the standard equation of a circle, explaining how to determine the center and radius from the equation. It provides examples of writing circle equations from given data, graphing circles, and converting equations to standard form by completing the square. The tutorial also includes methods for proving if points lie on a circle and using circle intersections to find an epicenter.

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

• x^2 + y^2 + r^2 = 0

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = r^2

• (x + h)^2 + (y + k)^2 = r

Tags

CCSS.HSG.GPE.A.1

How do you find the radius from a graph?

• It's the square root of the sum of the squared distances from the center to any two perpendicular points on the circle

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

• Count the units from the center to any point on the circle

• Measure the diameter and divide by 2

Tags

CCSS.HSG.GPE.A.1

What is the result of squaring the radius in the equation of a circle?

• The value on the right side of the equation

• The area of the circle

• The diameter of the circle

• The circumference of the circle

Tags

CCSS.HSG.GPE.A.1

What does the center of a circle represent in its equation?

• The highest point on the circle

• The point from which all measurements are made

• The intersection of the diameters

• The point (h, k) in the equation (x - h)^2 + (y - k)^2 = r^2

Tags

CCSS.HSG.GPE.A.1

What is the distance formula used for in the context of circles?

• To calculate the area of the circle

• To calculate the circumference

• To find the circle's diameter

• To determine the radius from the center to a point on the circle

Tags

CCSS.HSG.GPE.A.1

How is the radius found when given a point on the circle and the center?

• By subtracting the y-coordinate of the point from the y-coordinate of the center

• By adding the coordinates of the center and the point

• By finding the midpoint between the center and the point

• By using the distance formula between the two points

Tags

CCSS.HSG.GPE.A.1

What does completing the square help to find in a circle's equation?

• The circle's diameter

• The circle's circumference

• The area of the circle

• The center and radius from a general equation

Tags

CCSS.HSG.GPE.A.1

How can you prove a point lies on a circle?

• By calculating the area of the circle

• By drawing a line from the point to the center and measuring its length

• By showing the point's coordinates satisfy the circle's equation

• By measuring the distance from the point to the center

Tags

CCSS.HSG.GPE.A.1

How do you graph a circle given its equation?

• By calculating the area and drawing a circle with that area

• By plotting points that satisfy the equation

• By finding the center and radius and then drawing the circle

• By drawing a square and inscribing the circle

Tags

CCSS.HSG.GPE.A.1

What method is used to transform a general equation of a circle to its standard form?

• The quadratic formula

• Simplification

• Completing the square

• Factoring

Tags

CCSS.HSG.GPE.A.1