Find the Center and Radius of the Circle in Standard Form Easy Medium Hard

The video tutorial covers finding the center and radius of a circle in standard form. It begins with a simple example where the circle's center is at the origin, explaining the equation x^2 + y^2 = r^2. The tutorial then moves to more complex examples involving transformations, where the center is not at the origin. It emphasizes common mistakes students make, such as misinterpreting the signs of the center coordinates and incorrectly calculating the radius. The video concludes with a fun problem involving fractions and transformations, reinforcing the concepts learned.

What is the center of a circle with the equation x^2 + y^2 = 7?

• (1, 1)

• (2, -2)

• (-1, 2)

• (0, 0)

If R^2 = 7, what is the correct value of the radius R?

• 7

• 14

• 49

• √7

In the equation (x - 1)^2 + (y + 2)^2 = R^2, what is the center of the circle?

• (-1, 2)

• (1, -2)

• (1, 2)

• (-1, -2)

How do you rewrite an addition problem as a subtraction problem in the context of circle equations?

• By dividing by one

• By subtracting a negative number

• By multiplying by zero

• By adding a positive number

What is the radius of a circle with the equation (x - 0)^2 + (y - 2)^2 = 25?

• 25

• 5

• √25

• 10

In a circle equation with no transformation on x, what does this imply about the center?

• The center is shifted left

• The center is shifted right

• The center remains at x = 0

• The center is at y = 0

If a circle's equation is transformed such that y is affected but x is not, what happens to the center?

• The center remains unchanged

• The center moves up or down

• The center moves right

• The center moves left