show that the following Four Points in each of the following are concyclic and find the equation of the circle on which the lie (1,1),(-6,0),(-2,2),(-2,
-8)
Answers
Given : Four Points (1,1),(-6,0),(-2,2),(-2,-8)
To Find : Show that points are concyclic
Solution:
Take any three points :
Let say (1,1),(-6,0),(-2,2)
Find equation of circles passing through these
(x - h)² + ( y - k)² = r²
( 1- h) ² + ( 1 - k)² = r²
( -6- h) ² + ( 0 - k)² = r²
( -2- h) ² + ( 2 - k)² = r²
On solving these
h = -2 , k = - 3
Putting in any equation r² = 5²
Hence circle is
( x + 2)² + ( y + 3)² = 5²
Lets check whether 4th point lies on this circle or not
(-2,-8)
( -2 + 2)² + ( -8+ 3)² = 5²
=> 0² + 5² = 5²
Satisfied
Hence 4th point also lies on the circle
Hence points are concyclic
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