Logical Concepts of Consequence and Equivalence

The video tutorial explains the general formula for the equation of a circle, X^2 + Y^2 = R^2, and its derivation using the Pythagorean theorem. It demonstrates how to solve for missing values on a circle and addresses more complex problems, such as finding the equation of a circle with a given point on its circumference and determining whether another point lies inside or outside the circle.

What is the general formula for the equation of a circle centered at the origin?

• X^2 + Y = R^2

• X + Y = R^2

• X^2 + Y^2 = R^2

• X^2 + Y^2 = R

How can the radius of a circle be determined if a point on the circle is known?

• By using the slope formula

• By using the Pythagorean theorem

• By using the distance formula

• By using the midpoint formula

If a circle has a radius of 5 and an X-coordinate of -2, what are the possible Y-coordinates?

• ±√21

• ±√16

• ±√29

• ±√25

What is the equation of a circle with a point (-5, 3) on its circumference?

• X^2 + Y^2 = 25

• X^2 + Y^2 = 34

• X^2 + Y^2 = 29

• X^2 + Y^2 = 40

How do you determine if a point lies inside or outside a circle?

• By comparing the distance from the origin to the point with the radius

• By finding the midpoint between the origin and the point

• By checking if the point is on the X-axis

• By calculating the slope of the line from the origin to the point

What is the value of C^2 if point B (2, -6) is checked against a circle with R^2 = 34?

• C^2 = 25

• C^2 = 29

• C^2 = 40

• C^2 = 34

If a point's C^2 value is greater than R^2, where does the point lie?

• At the center of the circle

• Inside the circle

• On the circle

• Outside the circle