Asked by Emily
Find the area of the region inside the circle x^2+y^2=2 AND above the line y=1.
Answers
Answered by
Reiny
the radius of the circle is √2
Join radii to the points where the line y=1 cuts the circle.
from the origin to the line along the y-axis is 1, the radius is √2, so the other side of the triangle must be 1.
so you have a 45, 45 90 triangle, so is the other one
Both of them make a 90º at the centre.
the area of those two triangles is 1/2(2)(1) = 1
The area of the sector with the 90 angle is 1/4(the circle) = 1/4(2pi) = pi/2
So the area of the part above the line is
pi/2 - 1
Join radii to the points where the line y=1 cuts the circle.
from the origin to the line along the y-axis is 1, the radius is √2, so the other side of the triangle must be 1.
so you have a 45, 45 90 triangle, so is the other one
Both of them make a 90º at the centre.
the area of those two triangles is 1/2(2)(1) = 1
The area of the sector with the 90 angle is 1/4(the circle) = 1/4(2pi) = pi/2
So the area of the part above the line is
pi/2 - 1
Answered by
Emily
Ohh!! That makes perfect sense. Thanks so much for helping Reiny :-) I appreciate it!
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