Question

The centre is on the line 8x + 5y = 0 and the circle passes through the points (2)
(3,5).​

Answer 1

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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