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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
At what points will the line y = x intersect the unit circle x2 + y2 = 1?
Solution:
The two equations given are
y = x …. (1)
x2 + y2 = 1 …. (2)
Substitute equation (1) in (2)
x2 + x2 = 1
2x2 = 1
x2 = 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
y1= x1= 0.707
y2= x2 = -0.707
Therefore, the line y = x intersects the unit circle x2 + y2 = 1 at (0.707, 0.707) and (-0.707, -0.707).
At what points will the line y = x intersect the unit circle x2 + y2 = 1?
Summary:
The line y = x intersects the unit circle x2 + y2 = 1 at (0.707, 0.707) and (-0.707, -0.707).
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