Centre is on line 8x+5y=0 and the circle passes through the point (2,1),(3,5(
Answers
Given : The centre is on the line 8x + 5y = 0 and the circle passes through the points (2 , 1) (3,5).
To Find : Center of Circle
Solution:
point ( 2 ,1 ) and ( 3 , 5) lies on circle
line joining point will be chord
perpendicular bisector of chord passes through center of circle
mid point of ( 2 ,1 ) and ( 3 , 5)
= ( 2.5 , 3)
Slope = ( 5 - 1)/(3 - 2) = 4
slope of perpendicular line = -1/4
y - 3 = (-1/4)(x - 2.5)
=> 4y - 12 = -x + 2.5
=> x + 4y = 14.5
=> 8x + 32y = 116
8x+5y=0
=> 27y = 116
=> y = 116/27
x = -145/54
center of circle is (-145/54 , 116/27)
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