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a system of circles pass through (2,3) and have their centres on the line x+2y-7=0. show that the chords in which the circles of the system intersect the circle x2+y2-8x+6y-9=0 are concurrent and also find the point of concurrency

a system of circles pass through (2,3) and have their centres on the line x+2y-7=0. show that the chords in which the circles of the system intersect the circle x2+y2-8x+6y-9=0 are concurrent and also find the point of concurrency

Grade:12th pass

1 Answers

Vikas TU
14149 Points
7 years ago
write the center of the system of circles in the form of parametric .i.e
(7 – 2y ,y) 
And find the distance from (2,3) for radii.
Now u have center and radii in terms of k replace y by k.
write the circle eqn. therfore,
After 
this,
try
 
S1 – S2 =0 as the chord is concurrent.

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