Home
Class 12
MATHS
Find the area of the region in which poi...

Find the area of the region in which points satisfy
`3 le |x| + |y| le 5.`

Text Solution

Verified by Experts

The correct Answer is:
32 sq. units
We have `3 le |x|+|y| le 5`.
`|x|+|y| le 5` means that points lie inside the square endpoints of whose diagonal are `(+-5,0) " and " (0,+-5).`
`|x|+|y| ge 3` means that points lie outside the square endpoints of whose diagonal are `(+-3,0) " and " (0,+-3).`
So, common region is as shown in the figure.

`"Area of region" =4((1)/(2) xx 5 xx 5-(1)/(2) xx 3 xx 3) = 32 "sq.units"`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise 2.5|8 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise 2.6|5 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise 2.3|7 Videos

  • STRAIGHT LINE

    CENGAGE|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

Similar Questions

Explore conceptually related problems

Find the area of the region in which the points satisfy the inequaties 4ltx^2+y^2lt16 and 3x^2-y^2ge0 .

Sketch the regions which points satisfy |x+y| ge 2 .

Find tha area of the region containing the points (x, y) satisfying 4 le x^(2) + y^(2) le 2 (|x|+ |y|) .

Shade the regions where points satisfy |x-y| lt 1 .

x-y le 2

Find the area of the region {(x , y): 0 le y le x^(2)+1, 0le y le x +1, 0lex le2}

Find the area of the region {(x,y): y^(2) le 4x, 4x^(2) + 4y^(2) le 9} .

Plot the region satisfying |x|+ |y| le 2 and |x|+|y| gt 2 .

Find the area of the region bounded by the x-axis and the curves defined by y = tanx , (where (-pi)/(3) le x le (pi)/(3) ) and y = cotx .(where (pi)/(6) le x le (2pi)/(3) )

Solve 1 le |x-2| le 3