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DIRECTIONS for the question: Solve the following question and mark the best possible option.
The graph of x2 + y2 = 29 and the curve xy = 10 interest at certain number of points. All these points of intersection are joined successively by line segments to form a convex polygon. Which of the following best describes the polygon thus obtained?
  • a)
    Rectangle
  • b)
    Square
  • c)
    Hexagon
  • d)
    Rhombus
Correct answer is option 'A'. Can you explain this answer?
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DIRECTIONS for the question:Solve the following question and mark the ...
Given equation x2 + y2 = 29 is a circle with radius  units and the given equation xy = 10 is a rectangular hyperbola. The graphs of these two equations are as follows.

 
Given x2 + y2 = 29 and xy = 10
► (x+y)2 = x2 + y2 +2xy = 49
► x + y = 7 or -7   →  (i)
► (x-y)2 = x2 + y2 – 2xy = 9
► ∴ x – y = 3 or -3  →  (ii)
Form (i) and (ii), we get
► (x, y) = (5,2) or (2,5) or (-5, -2) or (-2, -5).
Distance between (5, 2) or (2, 5) = Distance between (-5, -2) and (-2, -5)   → (i)
Distance between (5, 2) and (-2, -5) = Distance between (-5, -2) and (2,5)  → (ii)
As the pairs of opposite sides are equal and (ii) > (i), i.e., adjacent sides are not equal, the points of intersection can either form a rectangle or a parallelgram, but only rectangle is given in the options.
► Note: Even if the above graph cannot be visualized, the question can still be answered by solving the two equations.
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DIRECTIONS for the question:Solve the following question and mark the ...
Explanation:

The given equations are:
1. x^2 + y^2 = 29
2. xy = 10

To find the points of intersection, we can substitute the value of y from equation 2 into equation 1:

x(x * 10/x) = 10
10x = 10
x = 1

Substituting this value of x into equation 2, we get:
y = 10/1
y = 10

Therefore, the points of intersection are (1, 10) and (10, 1).

Step 1: Plotting the points
Plot the points (1, 10) and (10, 1) on a coordinate plane.

Step 2: Find the other two points of intersection
To find the other two points of intersection, we can substitute the value of y from equation 2 into equation 1:

x(x * 10/x) = 29
10x = 29
x = 29/10

Substituting this value of x into equation 2, we get:
y = 10/(29/10)
y = 100/29

Therefore, the other two points of intersection are (29/10, 100/29) and (100/29, 29/10).

Step 3: Connect the points
Join the points of intersection successively by line segments.

Step 4: Determine the shape of the polygon
The polygon formed by joining the points of intersection is a rectangle.

Conclusion:
Therefore, the best description of the polygon obtained is a rectangle.
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DIRECTIONS for the question:Solve the following question and mark the best possible option.The graph of x2 + y2 = 29 and the curve xy = 10 interest at certain number of points. All these points of intersection are joined successively by line segments to form a convex polygon. Which of the following best describes the polygon thus obtained?a)Rectangleb)Squarec)Hexagond)RhombusCorrect answer is option 'A'. Can you explain this answer?
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DIRECTIONS for the question:Solve the following question and mark the best possible option.The graph of x2 + y2 = 29 and the curve xy = 10 interest at certain number of points. All these points of intersection are joined successively by line segments to form a convex polygon. Which of the following best describes the polygon thus obtained?a)Rectangleb)Squarec)Hexagond)RhombusCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONS for the question:Solve the following question and mark the best possible option.The graph of x2 + y2 = 29 and the curve xy = 10 interest at certain number of points. All these points of intersection are joined successively by line segments to form a convex polygon. Which of the following best describes the polygon thus obtained?a)Rectangleb)Squarec)Hexagond)RhombusCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for the question:Solve the following question and mark the best possible option.The graph of x2 + y2 = 29 and the curve xy = 10 interest at certain number of points. All these points of intersection are joined successively by line segments to form a convex polygon. Which of the following best describes the polygon thus obtained?a)Rectangleb)Squarec)Hexagond)RhombusCorrect answer is option 'A'. Can you explain this answer?.
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