Question

Examine the diagram and information to answer the question.


A circle in the coordinate plane has a radius of 5 and a center at point (5,4).

Point (x,y) lies on the circle.

The triangle formed by points (5,4), (5,y) and (x,y) is a right triangle.




What is the equation of the circle?


Match the expression or equation to the steps used to find the equation of the circle

Answer 1

Answer:

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

Step-by-step explanation:

The length of the vertical leg of the triangle shown is the difference between the y-coordinates y and 4:  (y - 4); the length of the horizontal leg is (x - 5).

The hypotenuse has length 5.

Applying the Pythagorean Theorem a^2 + b^2 = c^2, we get:

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