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`

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}=(-x)/(y)`

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

`\frac{\mathrm{d} y}{\mathrm{d} x}=(-1)/(1)`

Equation of line with slope

`m=(y-y_0)/(x-x_0)`

`-1=(y-1)/(x-1)`

`y+x=2`