Mastering the Equation of a Circle with Desmos

This video tutorial covers how to use Desmos to solve circle equations for the digital SAT Math. It begins with an introduction to Desmos, followed by step-by-step instructions on finding the center and radius of a circle. The tutorial also demonstrates how to check if specific points lie on a circle and addresses more complex problems involving completing the square. The video concludes with tips for using Desmos effectively in SAT Math preparation.

What is the first step to find a circle's radius using Desmos?

• Add the x-coordinates of the diameter's endpoints.

• Use the midpoint function directly.

• Multiply the diameter by two.

• Subtract the y-coordinates of the diameter's endpoints and divide by two.

Which function in Desmos helps to find the center of a circle?

• The radius function.

• The distance function.

• The circle equation solver.

• The midpoint function.

What is the radius of a circle if its diameter endpoints are (2, 1) and (2, -13)?

• 14

• 7

• 6

• 28

How can you verify if a point lies on a circle using Desmos?

• Inputting the point's coordinates into the circle's equation.

• Calculating the distance from the point to the circle's center.

• Typing the point into Desmos and observing if it intersects the circle.

• By checking if the point aligns with the circle's circumference.

What makes Desmos particularly useful for SAT Math circle questions?

• The educational tutorials it offers.

• Its ability to solve equations symbolically.

• The visual representation it provides for equations.

• Its built-in calculator functions.

Why might Desmos be preferred over manual calculations for some SAT questions?

• It is faster for all types of calculations.

• It requires less understanding of the math involved.

• It can handle complex problems involving completing the square more easily.

• It is always more accurate than manual calculations.

What is the center of a circle with diameter endpoints at (1, 5) and (1, -1)?

• (0, 2)

• (1, 3)

• (1, 2)

• (2, 1)

How can Desmos assist with SAT Math questions involving fractions?

• Through visual representation of fraction-based equations.

• By automatically simplifying fractions.

• It cannot assist with fractions.

• By providing tutorials on fraction operations.

What is the radius of a circle if its diameter endpoints are (-0.5, 9.5) and (-0.5, -10.5)?

• 10

• 15

• 20

• 5

Where can students find more resources for SAT Math preparation mentioned in the video?

• In the video comments.

• Within the Desmos app.

• On the SAT official website.

• In the video description.