Understanding Circle Equations and Coverage Areas

The video tutorial explores a circle-related word problem involving a cell phone tower with a 12-mile radius. The tower is located at (-3, 5) on a coordinate plane. The tutorial guides viewers through writing the standard equation of the circle and determining if a point (8, 0) is within the coverage area using the distance formula. The calculated distance is 12.08 miles, slightly exceeding the 12-mile radius, indicating the point is outside the service range.

What is the radius of the cell phone tower's coverage area?

• 20 miles

• 15 miles

• 12 miles

• 10 miles

Where is the cell phone tower located on the coordinate plane?

• (5, -3)

• (0, 0)

• (3, -5)

• (-3, 5)

What is the standard form of the equation for the circle with center (-3, 5) and radius 12?

• (x - 3)^2 + (y + 5)^2 = 144

• (x + 3)^2 + (y - 5)^2 = 144

• (x - 3)^2 + (y - 5)^2 = 144

• (x + 3)^2 + (y + 5)^2 = 144

What is the purpose of using the distance formula in this problem?

• To determine if a point is inside the circle

• To locate the center of the circle

• To find the radius of the circle

• To calculate the area of the circle

What is the distance formula used in this context?

• √((x2 + x1)^2 + (y2 + y1)^2)

• (x2 + x1)^2 + (y2 + y1)^2

• (x2 - x1) + (y2 - y1)

• √((x2 - x1)^2 + (y2 - y1)^2)

What is the calculated distance from the center to the point (8, 0)?

• 11.5 miles

• 12 miles

• 12.08 miles

• 13 miles

Is the point (8, 0) inside the coverage area of the cell phone tower?

• No, it is outside

• Yes, it is inside

• It is not possible to determine

• It is exactly on the boundary

What conclusion can be drawn from the distance calculation?

• The point is outside the circle

• The point is inside the circle

• The point is at the center of the circle

• The point is on the circle

What is the significance of the radius in determining the coverage area?

• It sets the boundary for coverage

• It determines the circumference

• It defines the diameter

• It is irrelevant to coverage

What is the final verdict regarding the cell phone user's location?

• On the boundary

• Outside the coverage area

• At the center

• Inside the coverage area