Question

find all of the points of the form (x, −x) which are 1 unit from the origin.

Answer 1

To be 1 unit from the origin, points must lie on the unit circle, or 
x^2+(-x)^2=1
x=+/- sqrt(2)
If the point is restricted to the form (x,-x), then
x=sqrt(2)  => P1=(sqrt(2),-sqrt(2))
x=-sqrt(2) => P2=(-sqrt(2),sqrt(2))

Therefore there are two such points.

Answer 2

The points are (1/√2,-1/√2) and (-1/√2,1/√2).

What is  the equation of circle ?

The equation of the circle is,

x²+y²=r²

where 'r' said to be the radius of the circle.

Now  solve the given question, we following the steps,

we have the point on the circle with radius 1 unit and centre(0,0),

The equation of the circle is,

x²+y²=r²

Given to be  (x,-x) and r=1, put the values on the circle equation

we have

x²+(-x)²=1²

x²+x²=1

2x²=1

x²=1/2

x=±(1/√2)

So the points are in the form (x,-x),

when x=1/√2, then point is  (1/√2,-1/√2)

when x=-1/√2, then point is  (-1/√2,1/√2)

Hence the points are (1/√2,-1/√2), (-1/√2,1/√2)

Learn more about circle equation from:

https://brainly.com/question/4870531

#SPJ2