Question

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 (r, s) and a point on the circle at (x, y). Show all necessary math work.

Part B: If (r, s) = (7, –4) and t = 10, determine the domain and range of the circle.

Part C: Is the point (9, 1) inside the border of the circle if (r, s) = (7, –4) and t = 10? Explain using mathematical evidence.

Answer 1

Explanation:

a)

(x - r)² + (y - s)² = t²

b)

(x - 7)² + (y + 4)² = 10²

Domain = r - t = 7 - 10 = -3

and r + t = 7 + 10 = 17

[-3, 17]

Range = s - t = -4 - 10 = -14

and s + 1 = -4 + 10 = 6

[-14, 6]

c)

yes, point (9,1) is inside the border of the circle.

x = 9 is in the domain and y = 1 is in the range.

But also, (9 - 7)² + (1 + 4)² = 29 < 10²