Given: Equation of circle is x2+y2+6x−4y−3=0 and point (5,1) If we substitute x=5 and y=1 in the expression x2+y2+6x−4y−3, we get ⇒52+12+6.5−4.1−3=49>0 .......(1) So, the point (5,1) is an external point. As we know that, the length of the tangent from an external point P(x1,y1) to the circle represented by the equation: x2+y2+2gx+2fy+c=0 is given by: √x12+y12+2gx1+2fy1+c Here, x1=5 and y1=1 and from equation (1) we know that, x12+y12+6x1−4y1−3=49 So, the length of the tangent is √49=±7 units ∵ The length cannot be negative. So, the length of tangent is 7 units Hence, option C is the correct answer.