If the point of intersection of the tangents drawn at the points where the line 5 x+y+1=0 cuts the circle x^2+y^2-2 x-6 y-8=0 is ( a, b ) , then 5 a+b=

Step-by-step solution

Given circle, x^2+y^2-2 x-6 y-8=0 So, chord of contact of two tangents drawn from the point P(a, b) to the given circle is gathered x a+y b-(x+a)-3(y+b)-8=0 (a-1) x+(b-3) y-(a+3 b+8)=0 gathered As, this line coincides with 5 x+y+1=0 array ll & a-1 5 = b-3 1 = -(a+3 b+8) 1 & a-1=-5(a+3 b+8) and & b-3=-a-3 b-8 & 6 a+15 b=-39 and a+4 b=-5 array On solving Eqs. (i) and (ii), we get a=-9 and b=1 Hence, 5 a+b=-45+1=-44