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What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?
  • a)
    1 - (π/2) sq. units
  • b)
    (π/3) - 1 sq. units
  • c)
    1 - (π/4) sq. units
  • d)
    π - 1 sq. units
Correct answer is option 'C'. Can you explain this answer?
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What is the area of a plane figure bounded by circle centered at orig...
To find the area of the plane figure bounded by the circle and the line, we first need to find the points of intersection between the circle and the line.

The line Max(x, y) = 1 can be rewritten as two separate lines: x = 1 and y = 1.

To find the points of intersection, we substitute these equations into the equation of the circle:

x^2 + y^2 = 1

For x = 1, we have:

1^2 + y^2 = 1
y^2 = 0
y = 0

So, one point of intersection is (1, 0).

For y = 1, we have:

x^2 + 1^2 = 1
x^2 + 1 = 1
x^2 = 0
x = 0

So, another point of intersection is (0, 1).

Now, we have the two points of intersection: (1, 0) and (0, 1). These two points divide the circle into two segments.

To find the area of the bounded figure, we calculate the area of each segment and sum them.

The first segment is a triangle with base 1 and height 1 (formed by the points (1, 0), (0, 0), and (0, 1)). The area of a triangle is given by:

Area = (base * height) / 2
Area = (1 * 1) / 2
Area = 1/2

The second segment is a sector of the circle with radius 1 and central angle 90 degrees (formed by the points (0, 0), (1, 0), and (0, 1)). The area of a sector is given by:

Area = (radius^2 * angle) / 2
Area = (1^2 * 90) / 2
Area = 45

So, the total area of the bounded figure is:

Total Area = Area of Triangle + Area of Sector
Total Area = 1/2 + 45
Total Area = 45.5 square units
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Community Answer
What is the area of a plane figure bounded by circle centered at orig...
Since x, y>0 thus we are talking of area in first quadrant only.
By definition the lines max, (x, y) = 1 means x = 1 and y £ 1 or y = 1 and x £ 1
Required area is shaded area as shown in the figure
= Area of square - Area of semicircle = 1 - (π/4) sq. units
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What is the area of a plane figure bounded by circle centered at origin having radius unity and the points of the lines represented by Max (x, y) = 1 where Max denotes Maximum of the two numbers x & y where x, y > 0?a)1 - (π/2) sq. unitsb)(π/3) - 1 sq. unitsc)1 - (π/4) sq. unitsd)π - 1 sq. unitsCorrect answer is option 'C'. Can you explain this answer?
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