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^2 + 1)^2 = 9(l^2 + m^2) implies |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.
Answer the following question based on above passage :
If `16m^2 - 8l - 1 = 0`, then equation of the circle having lx + my + 1 = 0 is a tangent is

Options

A. `(5/3, 0), (3-1)`
B. `(5/7, 5/7), (4, -3/4)`
C. `(5/3, 0), (4, -3/4)`
D. `(5/7, 5/7), (3, -1)`

Answer

D