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Let the lines (y-2)=m1(x-5) and (y+4)=m2...

Let the lines `(y-2)=m_1(x-5)` and `(y+4)=m_2(x-3)` intersect at right angles at `P` (where `m_1 and m_2` are parameters). If the locus of `P` is `x^2+y^2+gx+fy+7=0` , then the value of `|f+g|` is__________

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Verified by Experts

The correct Answer is:
6
Clearly, the locus of the point of intersection of lines is
`(x-5)(x-3) +(y-2) (y+4) =0`
or `x^(2)+y^(2)-8x+2y+7=0`
Hence, `|f +g| = | 2 + (-8) | = 6`
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