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A right triangle is shown in the graph.
Part A: Use the Pythagorean Theorem to derive the standard equation of the circle, with center at (f, g) and a point on the circle at (x, y). Show all necessary math work.

Part B: If (f, g) = (3, –1) and h = 8, determine the domain and range of the circle.

Part C: Is the point (10, –4) inside the border of the circle if (f, g) = (3, –1) and h = 8? Explain using mathematical evidence.

A right triangle is shown in the graph Part A Use the Pythagorean Theorem to derive the standard equation of the circle with center at f g and a point on the ci class=

Respuesta :

Answer:

A. (x - f)² + (y - g)² = h²

B. (x - 3)² + (y + 1)² = 64

Domain: [3 - 8, 3 + 8] = [-5, 11]

Range: [-1 - 8, -1 + 8] = [-9, 7]

C. (10 - 3)² + (-4 + 1)² = 7² + (-3)² = 49 + 9

= 58 < 64

(10, -4) is inside the circle.

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