Question

30. Find the coordinates of the centre of the circle passing through the points (-2, 3),
(-4, 4) and (-5, 5). Also find its radius​

Answer 1

Answer:

Step-by-step explanation:

Let the center has coordinates (x,y)

Then r²=(x+2)²+(y-3)²...........(1)

r²=(x+4)²+(y-4)².....................(2)

r²=(x+5)²+(y-5)²...................(3)

From(1) and (2)

x²+y²+4x-6y+4+9=x²+y²+8x-8y+16+16

4x-2y= -3....................(4)

from(2) and (3)

x²+y²+8x-8y+16+16=x²+y²+10x-10y+25+25

2x-2y= -18.....................(5)

Subtracting (5) from(4)

2x=15, x=15/2

From(5)

15-2y=-18

-2y=-33, y=33/2

Thus coordinates of center are ( 15/2 , 33/2)

Putting the value of (x,y) in(1) we get

r²=(15/2+2)²+(33/2-3)²

=(19/2)²+(27/2)²

=1/4( 361+729)

=1090/4

r=√272.5 ≈16.50