Question

Which of the following are the co-ordinates of the centre of the circle passes through L( 1 , -7 ) , M( 1 , 3 ) and N ( 4 , -6 ). ​

Answer 1

Answer:

this is the example of your Question

Step-by-step explanation:

Given three points (1,2),(3,−4)and(5,−6)

Let the coordinates o centre be O(h,k)

The distance from the centre to a point on the circumference is equal to radius.

∴ OA=OB=OC

From distance formula

OA

2

=OB

2

(h−1)

2

+(k−2)

2

=h−3)

2

+(k+4)

2

h

2

−2h+1+k

2

−4k+4=h

2

−6h+9+k

2

+8k+16

−2h−4k+5=−6h+8k+25

4h−12k=20⟹h−3k=5⟶(1)

OB

2

=OC

2

(h−3)

2

+(k+4)

2

=(h−5)

2

+(k+6)

2

h

2

−6h+9+k

2

+8k+16=h

2

−10h+25+k

2

+12k+36

−6h+8k+25=−10h+12k+61

⟹4h−4k=36⟹h−k=9⟶(2)

−2k=−4

h−3k=5−h±k=−9

∴k=2∴h=11

∴ The Coordinates are (h,k)=(11,2)