Question

3. What are the coordinates of the points of tangency of the two tangent lines through the point (1,1) each tangent to the circle x^2+y^2=1?

Answer 1

Answer:$y+x=2$    

Step-by-step explanation:

Given

equation of circle $x^2+y^2=1$

Equation of tangent passing through (1,1)

Slope of tangent is given by differentiating equation of circle

$2x+2y\frac{\mathrm{d} y}{\mathrm{d} x}=0$

$\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{-x}{y}$

at $(x,y)=(1,1)$

$\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{-1}{1}$

Equation of line with slope

$m=\frac{y-y_0}{x-x_0}$

$-1=\frac{y-1}{x-1}$

$y+x=2$