The angle between the two tangents drawn from origin to the circle x^2+y^2-14 x+2 y+25=0 is

Step-by-step solution

Given equation of circle is aligned x^2+y^2-14 x+2 y+25 & =0 (x^2-14 x+49 )+ (y^2+2 y+1 )-49-1+25 & =0 (x-7)^2+(y+1)^2 & =25=5^2 aligned Radius of circle =5 Centre of circle =(7,-1) Distance between origin and centre aligned & = (7)^2+(-1)^2 = 50 =5 2 O P & =5 2 and P A=5 aligned Now, = A P O P = 5 5 2 = 1 2 =45^ Similarly, = P B O P = 5 5 2 = 1 2 =45^ + =90^ Thus, angle between two tangent drawn from origin to given circle is 90^ .