The angle between two tangents drawn from

the origin to the circle  $(x-7{)}^2+(y+1{)}^2=25,$ is

detailed solution

Correct option is C

The equation of any line through the origin ( 0, O)  isy=mx If it is a tangent to the circle (x−7)2+(y+1)2=52 then, 7m+1m2+1=5⇒(7m+1)2=25m2+1⇒24m2+14m−24=0This equation, being a quadratic inm, gives two values ofm,  say  m1  and m2  . These two values of mare the slopes of the tangents drawn from he origin to the given circle.   From (i), we have  m1m2=−1Hence, the two tangents are perpendicular Hence, the two tangents are perpendicular(x−7)2+(y+1)2=50  of the given circle. Hence, required angle is π/2