# At what points will the line y = x intersect the unit circle x^{2} + y^{2} = 1?

**Solution:**

The two equations given are

y = x …. (1)

x^{2} + y^{2} = 1 …. (2)

Substitute equation (1) in (2)

x^{2} + x^{2} = 1

2x^{2} = 1

x^{2} = ½

x = √1/2

x = ±0.707

As the square can be positive or negative we get x1 = 0.707 and x2 = -0.707

From equation (1) we know that y = x

y_{1}= x_{1}= 0.707

y_{2}= x_{2 }= -0.707

Therefore, the line y = x intersects the unit circle x^{2} + y^{2} = 1 at (0.707, 0.707) and (-0.707, -0.707).

## At what points will the line y = x intersect the unit circle x^{2} + y^{2} = 1?

**Summary:**

The line y = x intersects the unit circle x^{2} + y^{2} = 1 at (0.707, 0.707) and (-0.707, -0.707).