Question

try again (b): your answer is incorrect. the circle below has center p. the point (x, y) is on the circle as shown. (a) find the following. radius: 2 units center: (4, 5) value of a: x - 4 value of b: y - 5 (b) use the pythagorean theorem to write an equation relating the side lengths of the right triangle. write your answer in terms of x and y (with no other letters). (x - 4)² + (y - 5)² = (4)²

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), \(a^2 + b^2 = c^2\). Here, \(a = x - 4\), \(b = y - 5\), and the hypotenuse (radius) \(c = 2\).

Step2: Substitute values into theorem

Substitute \(a = x - 4\), \(b = y - 5\), and \(c = 2\) into \(a^2 + b^2 = c^2\). So we get \((x - 4)^2 + (y - 5)^2 = 2^2\) or \((x - 4)^2 + (y - 5)^2 = 4\).

Answer:

\((x - 4)^2 + (y - 5)^2 = 4\)