find the equation of those tangents to the circle x2+y2-2x-4y-4=0 which are parallel to the line 3x-4y-1=0

Line parallel to 3x-4y+6=0 is 3x-4y=c

Let c be any constant.

1. A tangent have only one common point with circle.
2. Perpendicular distance of tangent from center of circle is equal radius.
3. Two tangent can be parallel.

Here equation of circle will be

(x-1)^2 +(y-2)^2 = 3^2.

So center of circle is (1,2)

Radius= 3

So distance of 3x-4y-c= 0 from (1,2) is equal to 3.

So,| (3–4*2-c)| /(3^2+4^2)^0.5 =3.

=> so c= -20 ,10.

So eqns will be

3x-4y=10 and

3x-4y=-20