Home
Class 12
MATHS
The are enclosed by 2|x|+3|y| le 6 is...

The are enclosed by `2|x|+3|y| le 6` is

A

3 sq. units

B

4 sq. units

C

12 sq. units

D

24 sq. units

Text Solution

Verified by Experts

The correct Answer is:
C
The given inequality is equivalent to the following system of inequalities.
`2x+3y le 6, "when " x ge 0, y ge0`
`2x-3y le 6, "when " x ge 0, y le0`
`-2x+3y le 6, "when " x le 0, y ge0`
`-2x-3y le 6, "when " x le 0, y le0`
which represents a rhombus with sides
`2x+-3y = 6 " and " 2x+- 3y=-6`
The lengths of the diagonals are 6 units and 4 units, respectively, along the x- and y-axes. Therefore, the required area is `1//2 xx 6 xx 4=12` sq. units.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise (Multiple)|30 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise (Comprehension)|27 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise 2.6|5 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

If f(x+y)=f(x)f(y)AA x,y in R and f(a)=2 then area enclosed by 3|x|+2|y|le8 is:

Statement I- The area by region |x+y|+|x-y|le2 "is" 4 sq units. Statement II- Area enclosed by region |x+y|+|x-y|le2 is symmetric about X-axis.

The area enclosed by the curvey y= cos 2x, 0 le x le (pi)/(4) and co-ordinate axes is 1/4 sq. unit.

Find the area of curve enclosed by |x+y|+|x-y|le4,|x|le1, y ge sqrt(x^(2)-2x+1) .

Let the straight line x = b divide the area enclosed by y = (1-x)^(2), y = 0 and x = 0 into two parts R_(1) (0 le x le b) and R_(2) (b le x le 1) such that R_(1) - R_(2) = 1/4 . Then b equals

Compute the area enclosed by the ellipse x= a cos t, y= b sin t(0 le t le 2pi)

(i) Draw a rough sketch of y = sin 2x and determine the area enclosed by the curve, x-axis and the lines x = (pi)/(4) and x = (3pi)/(4). (ii) Draw the graph of y = cos 3x, 0 lt x le (pi)/(6) and find the area between the curve and the axes.

The area enclosed between the curve y=sin^(2)x and y=cos^(2)x in the interval 0le x le pi is _____ sq. units.

CENGAGE-STRAIGHT LINES-Exercise (Single)
  1. Consider the points A(0,1)a n dB(2,0),a n dP be a point on the line 4x...

    Text Solution

    |

  2. Consider the point A= (3, 4), B(7, 13). If 'P' be a point on the line ...

    Text Solution

    |

  3. The are enclosed by 2|x|+3|y| le 6 is

    Text Solution

    |

  4. A B C is a variable triangle such that A is (1, 2), and Ba n dC on the...

    Text Solution

    |

  5. In A B C , the coordinates of the vertex A are (4,-1) , and lines x-y...

    Text Solution

    |

  6. P is a point on the line y+2x=1, and Qa n dR two points on the line 3y...

    Text Solution

    |

  7. If the equation of base of an equilateral triangle is 2x-y=1 and the v...

    Text Solution

    |

  8. The locus of a point that is equidistant from the lines x+y - 2sqrt2 =...

    Text Solution

    |

  9. If the quadrilateral formed by the lines a x+b y+c=0,a^(prime)x+b^(pri...

    Text Solution

    |

  10. A line of fixed length 2 units moves so that its ends are on the po...

    Text Solution

    |

  11. If the extremities of the base of an isosceles triangle are the points...

    Text Solution

    |

  12. A-=(-4,0),B-=(4,0)dotMa n dN are the variable points of the y-axis ...

    Text Solution

    |

  13. The number of triangles that the four lines y = x + 3, y = 2x + 3, y =...

    Text Solution

    |

  14. A variable line x/a + y/b = 1 moves in such a way that the harmonic me...

    Text Solution

    |

  15. Given A (0, 0) and B (x,y) with x in (0,1) and y>0. Let the slope of t...

    Text Solution

    |

  16. A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If la n ...

    Text Solution

    |

  17. Let P be (5, 3) and a point R on y=x and Q on the x-axis be such that ...

    Text Solution

    |

  18. If a pair of perpendicular straight lines drawn through the origin ...

    Text Solution

    |

  19. A point P(x,y) moves that the sum of its distance from the lines 2x-y-...

    Text Solution

    |

  20. If AD, BE and CF are the altitudes of Delta ABC whose vertex A is (-4,...

    Text Solution

    |