Question:
The set $\{(x, y) : x + y =1\}$ in the $xy$ plane represents
The set $\{(x, y) : x + y =1\}$ in the $xy$ plane represents
Updated On: Jun 8, 2024
- a square
- A circle
- An ellipse
- A rectangle which is not a square
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The Correct Option is A
Solution and Explanation
We have,
$|x|+|y|=1=\begin{cases}x +y=1, & x, y \in \text { I quadrant } \\ -x+ y=1, & x, y \in \text { II quadrant } \\ -x -y=1, & x, y \in \text { III quadrant } \\ x-y=1, & x, y \in \text { IV quadrant }\end{cases}$
Clearly, $A B C D$ is a square.
$|x|+|y|=1=\begin{cases}x +y=1, & x, y \in \text { I quadrant } \\ -x+ y=1, & x, y \in \text { II quadrant } \\ -x -y=1, & x, y \in \text { III quadrant } \\ x-y=1, & x, y \in \text { IV quadrant }\end{cases}$
Clearly, $A B C D$ is a square.
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Concepts Used:
Applications of Integrals
There are distinct applications of integrals, out of which some are as follows:
In Maths
Integrals are used to find:
- The center of mass (centroid) of an area having curved sides
- The area between two curves and the area under a curve
- The curve's average value
In Physics
Integrals are used to find:
- Centre of gravity
- Mass and momentum of inertia of vehicles, satellites, and a tower
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- The velocity and the trajectory of a satellite at the time of placing it in orbit
- Thrust