i did this all things
S1+lambdaS2=0
lambda≠-1
this gives p≠-1/2
so i went for option "2"
but many reputed coaching say "1" and some sub-standard ones say "2" so i think "1" is right but how??
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2 Answers
62x^2+y^2+3x+7y+2p-5+\lambda(x+5y+p^2+2p-5)=0 \\1+1+3+7+2p-5+\lambda(1+5+p^2+2p-5)=0 \\7+2p+\lambda(1+p)^2=0 \\\lambda=-(7+2p)/(1+p)^2
in the second step, we have said that this curve passes through (1,1)
in the 1st step i have taken s1+lamda(s2-s1) whcih is effectively same as s1+lambda(s2)
so for each value of p, we have one lambda and hence one such circle... the only value of p is -1 for whcih we dont have such a circle....
62Why the previous solution is not exact......
See that the circles if they intersect then the line joining the two points of intersection will alwys form a triangle unless the point (1,1) lies on the radical axis..
The only problem will be when these circles dont intersect
So we have to find the condition that the distance between the centers is greater than the sum of radii or that the distance is less that the difference of the radii..
Solve the second condition and you are there :)