Question

WILL GIVE BRAINLIST 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.
Step 1: Find the length of the vertical leg of the right triangle

Step 2: Find the length of the horizontal leg of the right triangle.

Step 3: Use the Pythagorean Theorem to find the equation of the circle


answERS:
(x−3)2+(y−2)2=6^2
(x−2)2+(y−3)2=6^2
|y−3|
|y−2|
|x−3|
|x−2|

Answer 1

Answer:  To find the equation of the circle, it is not necessary to find the legs of the triangle first.  

The length of the legs (equal) is 3√2 or  4.243

Step-by-step explanation:

The equation for a circle is similar to the Pythagorean Theorem

       a²   +   b²     = c²

( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.

The a and b terms are  changed to allow insertion of  h and k to locate the center of the circle on a Cartesian plane.

You can get the information needed from

Given: radius =6 and  "a center at the point (3,2)"

Substitute  3 for h and  2 for k  and  6 for r

( x - 3 )² + ( y - 2 )² = 6²    This is the equation of the circle .

From the diagram, it appears that x-3 = y-2

So, in the equation, we can substitute 2(x²) = 36

x² = 36/2 .   x² = 18

√x² = √18 = √9(2)

x = 3√2   =4.2426

the length of the horizontal leg is 4.243

Substitute for x in to find  x+3  the coordinate (x,2)

the coordinate x, 2 is  (7.24, 2)

Substitute for y in to find  y+2, the length of the vertical leg is 4.243.

y + 2 = 6.243  

So the coordinate (x,y) on the circle is (7.24, 6.24)

This does not account for Step 1 and  Step 2 in the question, matching expressions or equations to the steps. I hope you will be able to sort that our with the information here.