Question

!!HELP WILL GIVE BRAIN LIST!! Examine the diagram and information to answer the question. A circle in the coordinate plane has a radius of 6 and a center at the point (3,2). Point (x,y) lies on the circle. The triangle formed by points (3,2), (x,2) 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. answers TO fill IN the match |x−3| (x−2)2+(y−3)2=62 |x−2| |y−3| (x−3)2+(y−2)2=62 |y−2|

Answer 1

1. |y-2|
2. |x-3|
3. (x-3)²+(y-2)² = 36

Explanation:

1. The length of the vertical leg of the triangle is the magnitude of the difference between the y-coordinate of the point on the circle and the y-coordinate of the center:

|y -2|

2. The length of the horizontal leg of the triangle is the magnitude of the difference between the x-coordinate of the point on the circle and the x-coordinate of the center:

|x -3|

3. The Pythagorean theorem tells you the sum of the squares of the leg length is equal to the square of the hypotenuse length. The hypotenuse is given as 6, so the equation is ...

`|y-2|^2 +|x-3|^2=6^2`

Since the square of a number is the same as the square of its magnitude, we can write this as ...

`(x-3)^2+(y-2)^2=36`