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, indicating the point is outside the coverage area.

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

• 12 miles

• 10 miles

• 20 miles

• 15 miles

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

• (-3, 5)

• (5, -3)

• (0, 0)

• (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 does the circle represent in the context of the cell phone tower?

• The signal strength of the tower

• The area of the tower

• The coverage area of the tower

• The height of the tower

Which formula is used to determine if a point is within the coverage area?

• Volume formula

• Distance formula

• Circumference formula

• Area formula

What is the distance formula used in the video?

• (x2 - x1)^2 + (y2 - y1)^2

• sqrt((x2 - x1)^2 + (y2 - y1)^2)

• (x2 + x1)^2 + (y2 + y1)^2

• sqrt((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) within the coverage area of the tower?

• No, it is outside the area

• Yes, it is within the area

• It is exactly on the boundary

• It is not possible to determine

What is the significance of the calculated distance being 12.08 miles?

• It is irrelevant

• It is greater than the radius

• It is equal to the radius

• It is less than the radius

What conclusion is drawn about the cell phone user's location?

• The user is at the edge of the range

• The user is within the service range

• The user is outside the service range

• The user is at the center