Answer
a) (0,0), 1
b) $x^{2} + y^{2} = 1 $
c) i) 0, ii) 0, iii) 0, iv) 0
Work Step by Step
a) The equation of a circle is $({x-a})^{2} + ({y-b})^{2} = 1 $, a and b being the coordinates of the center point. a being the x-coordinate and b, the y-coordinate. For the unit circle, a=b=0
c) We want to satisfy the equation $x^{2} + y^{2} = 1 $, so we plug in each point as P(x,y) and solve for the missing component. For P(1,y), $1^{2} + y^{2} = 1$ so $y^{2}=1-1$ and $y=0 $
For P(x,1), $x^{2} + 1^{2} = 1$ so $x^{2}=1-1$ and $x=0 $
For P(-1,y), $(-1)^{2} + y^{2} = 1$ so $y^{2}=1-1$ and $y=0$
For P(x,-1), $x^{2} + (-1)^{2} = 1$ so $x^{2}=1-1$ and $x=0 $
