We are given the equations:
y = x
x^2 + y^2 = 1
Now to find the points where they will intersect, combine the two equations:
y^2 + y^2 = 1
2 y^2 = 1
y^2 = 0.5
y = 0.707
From equation 1:
x = y = 0.707
Hence the two functions will intersect at:
(0.707, 0.707)
or
(0.7, 0.7)
Answer:
the line y = x intercept the unit circle x^2+y^2=1 at points:
(0.707, 0.707) and (-0.707, -0.707)
Step-by-step explanation:
The points of intersection are the points that satisfy the both following equations:
equation 1: y = x
equation 2: x^2 + y^2 = 1
So, we can replace equation 1 on equation 2 as following:
x^2 + y^2 = 1
As well y = x then:
x^2 + x^2 = 1
Isolating x we obtain:
2x^2=1
x^2 = 1/2
[tex]x=\sqrt{\frac{1}{2} }[/tex]
x=±0.707
Taking into account that the squared can be positive or negative, we have two solutions for x: x1=0.707 and x2=-0.707
Finally for find the value of y1 and y2, we replace the value of x1 and x2 on any of the principal equations (equation 1 or 2).
For simplicity we replace on Equation 1 (y = x), so:
y1=x1=0.707 and y2=x2=-0.707
Concluding that the line y = x intercept the unit circle x^2+y^2=1 at points:
(0.707, 0.707) and (-0.707, -0.707)
