Circular conundrum

Geometry Level 4

{ x 2 + y 2 + 3 x + 7 y + 2 p − 5 = 0 x 2 + y 2 + 2 x + 2 y − p 2 = 0 \begin{cases} {x^2+y^2+3x+7y+2p-5=0} \\ {x^2+y^2 + 2x+2y-p^2 = 0 } \end{cases}

If P P and Q Q are the points of intersection of the circles given above for constant p p , then there is a circle passing through P , Q P,Q and ( 1 , 1 ) (1,1) for:

all except two values of p p all except one value of p p all values of p p exactly one value of p p no values of p p

Vineet Golcha by vineet golcha , 21, India

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