If `7l^(2)-9m^(2) + 8l + 1 = 0` and we have to find equation of circle having `lx + my + 1 = 0` is a tangent and we can adjust given condition as `16l^(2) + 8l + 1 = 9(l^(2) + m^(2))` or `(4l + 1)^(2) = 9(l^(2) + m^(2)) rArr (|1 4l+1|)/(sqrt((l^(2) + m^(2)))) = 3` Centre of circle = (4, 0) and radius = 3 when any two non parallel lines touching a circle, then centre of circle lies on angle bisector of lines.
On the basis of above information, answer the following questions :
If `16l^(2) + 9m^(2) = 24lm + 6l + 8m + 1` and if S be the equation of the circle having `lx + my + 1 = 0` is a tangent when the equation of director circle of S is

Options

A. `x^(2) + y^(2) + 6x + 8y = 25`
B. `x^(2) + y^(2) - 6x + 8y = 25`
C. `x^(2) + y^(2) - 6x - 8y = 25`
D. `x^(2) + y^(2) + 6x - 8y = 25`

Answer

C