Doubt from tests

AB is any chord of the circle x^2 + y^2 -6x -8y -11 = 0 , which subtend 90^{o} at (1,2). If locus of mid-point of AB is circle x^2 + y^2 - 2ax - 2by - c = 0, then find the value of a+b+c.

Answer not matching. Please help.

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@VenkatAmith

bro i am getting a negative number… @ThirdJuly

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Ans. is 7. I am getting 31. How did you do?

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i am getting -10, bro @ThirdJuly

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I am getting 8 now. I didn’t realise that (1,2) was inside the circle, but still answer is given 7.

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i am getting 5 now, i did once again (a small mistake)

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oh, didn’t notice answer is 7…

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sorry bro @LaveshGupta even i am getting 8

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Ya I did the same. Answer might be wrong.

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Let me try too.

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yes bro, let wait for others to respond

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Ya sure bro why not.

btw electrostatics wala smjh aaya? @LaveshGupta

Nahi.I didn’t login to brilliant lol.

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iam getting 9

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i think this is wrong please ignore


@manan_uppadhyay @Aastik_Guru @Amish_1706 @Abhinav.08 @VenkatAmith @Seshank @Navjeet_Kohli
In this question i got that any line of form ax+by+c=0 such that a,b,c in AP will pass through (1,-2) but problem is with radical axis , if we could prove somehow or find radical axis via image method and prove it is also of form ax+by+c=0 such a,b,c are in AP then the point of intersection of both will be (1,-2) for both lines and answer will satisfy it. Sorry for image quality , idk how to take screenshot from pc.

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Bro L1 is the radical axis of S1 and S2

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Can you explain kaise ? I knew has to be of form ax+by+c but wasnt able to find it.
Ok got it sorry , image hain dono toh tangents from L1 will be equal on both