The equations of the tangents drawn from (7, 1) 

to the circle $x^2+y^2=25$ are  

detailed solution

Correct option is A

The equation of any line through (7, 1) is y−1=m(x−7)⇒mx−y−7m+1=0                       (i)the coordinates of the centre and radius of the given circle are (0, 0) and 5 respectively.  The line (i) will touch the given circle, if, Length of the perpendicular from the centre = Radius ⇒m×0−0−7m+1m2+(−1)2=5⇒1−7mm2+1=5⇒(1−7m)2m2+1=25⇒24m2−14m−24=0⇒m=−3/4,4/3Substituting the values of m in (i), we obtain   −34x−y+214+1=0  and  43x−y−283+1=0 ⇒ 3x+4y−25=0  and  4x−3y−25=0which are the equations of tangents