Question

10. WEATHER On average, the circular eye of a hurricane is about 15 miles in diameter. Gale winds can affect an area up to 300 miles from the storm's center. A satellite photo of a hurricane's landfall showed the center of its eye on one coordinate system could be approximated by the point (80, 26).
a. Write an equation to represent a possible boundary of the hurricane's eye.

b. Write an equation to represent a possible boundary of the area affected by gale winds. ​

Answer 1

The equation to represent a possible boundary of the hurricane's eye is (x - 80)² + (y - 26)² = 7.5²

Circle Equation

The standard equation of a circle is given by:

(x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle and r is the radius.

Given that diameter = 15 miles, hence radius = 15/2  = 7.5. Also, center = (80, 26)

The equation of circle is:

(x - 80)² + (y - 26)² = 7.5²

The equation to represent a possible boundary of the hurricane's eye is (x - 80)² + (y - 26)² = 7.5²

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