Answer:[tex]y+x=2[/tex]
Step-by-step explanation:
Given
equation of circle [tex]x^2+y^2=1[/tex]
Equation of tangent passing through (1,1)
Slope of tangent is given by differentiating equation of circle
[tex]2x+2y\frac{\mathrm{d} y}{\mathrm{d} x}=0[/tex]
[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{-x}{y}[/tex]
at [tex](x,y)=(1,1)[/tex]
[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{-1}{1}[/tex]
Equation of line with slope
[tex]m=\frac{y-y_0}{x-x_0}[/tex]
[tex]-1=\frac{y-1}{x-1}[/tex]
[tex]y+x=2[/tex]
