Exploring the Equation of a Circle

What shape is formed when a cone is cut perpendicular to its axis?

• Ellipse

• Circle

• Hyperbola

• Parabola

Which conic section is formed by cutting a cone in a way that the plane is parallel to the sides of the cone?

• Hyperbola

• Ellipse

• Circle

• Parabola

What is the standard form equation of a circle centered at the origin with radius r?

• (x - h)^2 + (y - k)^2 = r

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = r

What changes in the equation of a circle when the center is not at the origin?

• The equation only includes the radius

• The equation includes the center coordinates (h, k)

• The equation remains the same

• The radius becomes zero

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

• (x - h)^2 + (y - k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r

• x^2 + y^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

How do you find the radius of a circle given a point on the circle and the center?

• Subtract the x-coordinates

• Use the midpoint formula

• Subtract the y-coordinates

• Use the distance formula

What is the purpose of completing the square in the context of circle equations?

• To calculate the circumference

• To determine the circle's center and radius

• To simplify the equation

• To find the circle's diameter

What is the result of completing the square for the equation x^2 - 6x + y^2 - 2y = 6?

• (x - 3)^2 + (y - 1)^2 = 1

• (x + 3)^2 + (y + 1)^2 = 10

• (x + 3)^2 + (y + 1)^2 = 1

• (x - 3)^2 + (y - 1)^2 = 10

How do you find the x-intercepts of a circle's equation?

• Use the distance formula

• Set y to zero and solve for x

• Set x to zero and solve for y

• Use the midpoint formula

How do you find the y-intercepts of a circle's equation?

• Use the midpoint formula

• Use the distance formula

• Set y to zero and solve for x

• Set x to zero and solve for y