Correct Answer - B
The equation of a line through P(1,2) is
`(x-1)/(cos theta)=(y-2)/(sin theta)`
The coordinates of point of this line at a distance of 3 units from P(1,2) are given by `(x-1)/(cos theta)=(y-2)/(sin theta)=pm3` . Letthe coordinates of the points be `(1 pm 3 cos theta, 2 pm sin theta)` . These points lie on `x+y=7`.
`(1 pm 3 cos theta)+(2 pm 3 sintheta)=7`
`implies pm3(cos theta + sin theta)=4`
`implies 9(1+sin 2theta)=16`
`implies (18tan theta)/(1+tan^(2)theta)=7`
`implies 7 tan^(2)theta-18 tan theta +7=0`
`implies tan theta ` is a root of `7x^(2)-18x+7=0`
