Question

3. Find the centre of a circle passing through the points (6-6).(3.-7) and (3.3).​

Answer 1

AnswEr:

Let the given points are A(6,-6) ,B(3,-7) ,C (3,3) & P(X,Y) is the centre of circle.

Here AP = BP = CP

Taking AP = BP

AP² = BP²

(x - 6)² + (y + 6)² = (x - 3)² + ( y + 7)²

x² - 12x + 36² + y² + 12y + 36 = x² - 6x² + 9 +y² + 14 y + 49

= -12x + 36 +12y + 36 = -6x + 9 +14y + 49

= -12x + 6x +12y -14y + 72 - 49 -9 = 0

= -6x -2y + 72 -58 = 0

= -6x - 2y +14 = 0

= -3x - y + 7 = 0 ______eq (1)

Again BP = CP

BP² = CP²

(x -3)²+ (y-7)² = (x -3)² + (y -3)²

= x² - 6x + 9+ y² + 14y +49 = x² - 6x + 9 + y² - 6y+9

= 6x + 9 + 14y + 49 = -6x + 9 - 6y + 9

= 14y + 6y + 49 - 9 = 0

= 20y + 40 = 0

= y = -40/20

= y =-2

Putting Value of y in eq (1)

3x + y -7=0

3x -2 -7 = 0

3x = 9

x = 3

Center of the Circle is ( 3,-2)