Find the equation of the tangent to the circle x²+y²-2x-y-15=0

x−2y+5=0

Step-by-step explanation:

x2+y2−2x+4y=15

differentiating both sides with respect to x

2x+2yy′−2+4y′=0

2x−2+(2y+4)y′=0

y′=2−2x2y+4

y′(−1,2)=2+24+4=12

slope of tangent at (- 1, 2)=12

Equation of the tangent is

y−2=12(x+1)

x−2y+5=0