How do i use the distance formula to show that the equation of the unit circle is given by x^2 + y^2 =1?

Question

anonymous · Answer

the definition of the unit circle is a circle with radius 1.
so if you want the locus of points that are all 1 unit away from (0, 0), use the distance formula for that...
do you know the distance formula?

anonymous · Answer

yes

anonymous · Answer

ths is the distance formula...
$$\large Distance=\sqrt {(x_2-x_1)^2+(y_2-y_1)^2} $$

anonymous · Answer

since you know the distance ( the distance is 1), and you know what 1 of those points are, (x1, y1) is (0, 0),  plug them all in to the distance formula...

anonymous · Answer

you'll get..
$$\large 1 = \sqrt{(x-0)^2+(y-0)^2} $$
now just square both  sides and simplify and you'll get the equation for the unit circle.

anonymous · Answer

|dw:1338924862731:dw|
solve this and get required  equation