Question

Find the equation of tangents to the circle x² + y² – 6x + 4y – 12 = 0 which are parallel to the line 4x + 3y + 5 = 0

Answer 1

Given circle is x² + y² – 6x + 4y – 12 = 0 .......(i) 

and given line is 4x + 3y + 5 = 0 .......(ii) 

Centre of circle (i) is (3, –2) and its radius is 5. 

Equation of any line 

4x + 3y + k = 0 parallel to the line (ii) .......(iii) 

If line (iii) is tangent to circle, (i) then

or 6 + k = ± 25 

∴ k = 19, – 31 

Hence equation of required tangents are 4x + 3y + 19 = 0 and 4x + 3y – 31 = 0