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A point P lies on or inside the circl...

A point `P` lies on or inside the circle `x^2+y^2-8x+7=0` and ellipse `25 x^2+4y^2=100` both. The point `P` moves such that its path encloses the greatest possible area is always at a fixed distance from point `(3/2,0)` in its region. If the locus of `P` is `a x^2+y^2+b x+c=0` then which of the following is/are correct? `a=2` b. `b=-3` c. `c=2` d. `a+b+c=0`

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