Question

Find the center of the circle passing through the points (6, -6), (3, -7) and (3, 3)

Answer 1

Hello users.......

Here given that
Points (6, -6), (3, -7) and (3, 3) are on the circumference of the circle.

We have to find
Centre of circle =?

Solution:-
Let O be the centre of circle = (x,y)

Because .
Points A(6, -6), B(3, -7) and C(3, 3) are on the circumference
=> OA = OB = OC ( radius of circle)

Using distance formula
OA = √(6-x)² + (-6-y)²
&
OB = √(3-x)² +(-7-y)²
&
OC =√(3-x)² +(3-y)²

Here OA = OB (radius)

=> √(6-x)² + (-6-y)²= √(3-x)² +(-7-y)²
=> (6-x)² + (-6-y)² = (3-x)² +(-7-y)²
=>36 +x² -12x + 36 +y² -12y = 9+ x² -6x + 49 +y² -14y
=> 72 -12x -12y = 58 -6x -14y
=> -6x +2y = -14............(1)

Now
OB = OC. (radius)

=> √(3-x)² +(-7-y)² = √(3-x)² +(3-y)²
=> (3-x)² +(-7-y)² = (3-x)² +(3-y)²
=> 9+ x² -6x + 49 +y² -14y = 9+x² -6x +9 +y² -6y
=> 58 -6x -14y = 18-6x -6y
=> -14y +6y = 18-58
=> -8y = -40
=> y= 5

Put the value of. y in equation ...........(1)
We get
-6x +2×5= -14
=> -6x = -14-10 = -24
=> x = 24/6= 4

Hence .
The centre of circle = (4 , 5) answer

✡⭐ Hope it helps ⭐✡