I need help solving this problem.
Question: At what points will the line y=-x intersect the unit circle x2+y2=1?
That circle equation would be x^2 + y^2 = 1
sub the y = -x into the circle
x^2 + x^2 = 1
2x^2 = 1
x^2 = 1/2
x = ±1/√2
if x = +1/√2, y = -1/√2
finish it up
To find the points where the line y=-x intersects the unit circle x^2+y^2=1, we can substitute the equation of the line into the equation of the circle and solve for the x-coordinate.
Substituting y=-x into the equation of the circle:
x^2 + (-x)^2 = 1
x^2 + x^2 = 1
2x^2 = 1
x^2 = 1/2
x = ±√(1/2)
Now, to find the corresponding y-coordinates, we substitute the obtained values of x back into the equation of the line.
When x = √(1/2):
y = -(√(1/2))
y = -√(1/2)
When x = -√(1/2):
y = -(-√(1/2))
y = √(1/2)
So, the points where the line y=-x intersects the unit circle x^2 + y^2 = 1 are (√(1/2), -√(1/2)) and (-√(1/2), √(1/2)).