Equation of given hyperbola,
`x^2-9y^2 = 9`
`=>x^2/9-y^2/1 = 1`
Now, equation of tangents can be given as,
`y = mx+-c`
Here, `c = +-sqrt(a^2m^2-b^2) = +-sqrt(9m^2-1)`
So, equation of tangents,
`y = mx+-sqrt(9m^2-1)->(1)`
Now, as tangents are drawn from `(3,2)`,
`:. 2 = 3m+-sqrt(9m^2-1)`
`=>(2-3m) = +-sqrt(9m^2-1)`
`=>(2-3m)^2 = 9m^2-1`
`=>4+9m^2-12m = 9m^2-1`
`=>12m = 5`
`=> m = 5/12`
Putting value of `m` in (1),
`y = 5/12x+-9/12`
`=>5x-12y+9 = 0 and 5x-12y-9 = 0`
So, above two are the equations of tangents to given hyperbola.
