Question

if the lines 2x+3y+1=0 and 6x+4y+1=0 intersect the co-ordinate axes in 4 points,then the circle passing through the points is​

Answer 1

Given : the lines 2x+3y+1=0 and 6x+4y+1=0 intersect the co-ordinate axes in 4 points,

To Find : the circle passing through the points  

Solution:

2x  + 3y + 1 = 0

x = 0  => y = -1/3

y = 0  => x = - 1/2

Points are

( 0 , - 1/3)  and ( -1/2  , 0)

6x+4y+1=0

x = 0  => y = -1/4

y = 0  => x = - 1/6

Points are

( 0 , - 1/4)  and ( -1/6  , 0)

Find perpendicular bisector of both the lines above  and from  intersection find centers

find distance between center and any point to find radius

(x - h)² + (y - k)² = r²

on solving get :

12x² + 12y² + 8x + 7y + 1 = 0  is the required equation

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