1.

If P and Q are the points of intersection of the circles `x^2+y^2+3x+7y+2p=0` and `x^2+y^2+2x+2y-p^2=0` then there is a circle passing through P,Q and (1,1) forA. all values of pB. all except one value of pC. all except two values of pD. exactly one value of p

Answer» Correct Answer - 2
`x^(2)+y^(2)+3x+7y+2p-5+lambda(x^(2)+y^(2)+2x+2y-p^(2))=0`, `lambda cancel(=) -1`,
passes through point of intersection of given circles.
Sincet it passes through `(1,1)`
`7-2p+lambda(6-p^(2))=0`
`implies 7-2p+6lambda -lambdap^(2)=0`
If `lambda = -1`, then
`7-2p-6+p^(2)=0`
`implies p^(2)-2p+1=0`
`:. p =1`
If `lambda cancel (=)-1` then `pcancel(=) 1`.
Therefore, all values of p are possible except `p=1`


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