Understanding Circles in the Coordinate Plane

This video tutorial covers the basics of working with circles in the coordinate plane. It includes graphing circles from equations, deriving equations from graphed circles, and verifying if points lie on a circle. The tutorial provides step-by-step examples to help understand the concepts of circle center, radius, and the general equation form.

What indicates that an equation represents a circle?

• The equation equals zero.

• The equation contains only linear terms.

• The presence of x squared and y squared terms on the same side of the equation.

• The presence of x and y terms on opposite sides of the equation.

What is the center of the circle for the equation x^2 + y^2 = 9?

• (3, 3)

• (0, 0)

• (1, 1)

• (-1, -1)

How do you determine the radius of the circle from the equation x^2 + y^2 = 9?

• By halving the constant term.

• By doubling the constant term.

• By taking the square root of the constant term.

• By squaring the constant term.

What is the radius of the circle with the equation x^2 + y^2 = 9?

• 4

• 3

• 2

• 5

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

• By finding the midpoint of a diameter.

• By finding the intersection of the tangents.

• By finding the intersection of the x and y axes.

• By finding the midpoint of the radius.

What is the equation of a circle with center (-3, 3) and radius 6?

• (x + 3)^2 + (y - 3)^2 = 36

• (x - 3)^2 + (y - 3)^2 = 36

• (x - 3)^2 + (y + 3)^2 = 36

• (x + 3)^2 + (y + 3)^2 = 36

What is the general form of the equation of a circle?

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r

• x^2 + y^2 = r

• (x - h)^2 + (y - k)^2 = r^2

How do you check if a point lies on a circle?

• By checking if the point is equidistant from the center.

• By measuring the angle at the center.

• By substituting the point into the circle's equation.

• By drawing a tangent at the point.

Does the point (8, -3) lie on the circle with the equation (x + 1)^2 + (y - 5)^2 = 50?

• Only if y is negative

• Only if x is positive

• No

• Yes

Does the point (-2, -2) lie on the circle with the equation (x + 1)^2 + (y - 5)^2 = 50?

• Only if y is negative

• Only if x is positive

• No

• Yes