Exploring Equations of Circles

What shapes are formed by the intersection of a plane and a cone?

• Cylinders and spheres

• Triangles and squares

• Circles, ellipses, parabolas, and hyperbolas

• Rectangles and trapezoids

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

• The center of the circle

• The vertex points

• The endpoints of the diameter

• The radius and diameter

In the equation of a circle, what does 'r' stand for?

• Diameter

• Radius

• Area

• Circumference

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

• x*h + y*k = 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 write the equation of a circle given the center and radius?

• Add the radius to the center coordinates

• Subtract the radius from the center coordinates

• Multiply the center coordinates

• Plug the center into 'h' and 'k', and square the radius

What is the correct equation form for a circle with center at (0, -2) and radius 7?

• x^2 + (y+2)^2 = 49

• x^2 + (y-2)^2 = 7

• (x-0)^2 + (y+2)^2 = 7

• (x+0)^2 + (y-2)^2 = 49

If given the endpoints of a diameter of a circle, how can you find the center?

• Subtract the coordinates of one endpoint from the other

• Average the x and y coordinates of the endpoints

• Multiply the coordinates of the endpoints

• Divide the coordinates of one endpoint by the other

What is the equation of a circle with a center at (2, 7) and a radius derived from the endpoint (5, 6)?

• (x-2)^2 + (y-7)^2 = 10

• (x+2)^2 + (y+7)^2 = 10

• (x-5)^2 + (y-6)^2 = 10

• (x-2)^2 + (y-7)^2 = 5

How do you determine the radius if only a center and a point on the circle are given?

• Subtract the center coordinates from the point's coordinates and square the result

• Add the center coordinates to the point's coordinates

• Use the midpoint formula on the center and the point

• Calculate the distance between the center and the point

What is the next step after finding the center using the endpoints of a diameter?

• Calculate the circumference

• Multiply the center coordinates

• Find the radius using the midpoint

• Use the center to find the radius with any endpoint