Home
Class 12
MATHS
A rhombus is inscribed in the region com...

A rhombus is inscribed in the region common to the two circles `x^2+y^2-4x-12=0` and `x^2+y^2+4x-12=0` with two of its vertices on the line joining the centers of the circles. The area of the rhombus is (a)`8sqrt(3)s qdotu n i t s` (b) `4sqrt(3)s qdotu n i t s` `6sqrt(3)s qdotu n i t s` (d) none of these

A

`8 sqrt(3)` sq. units

B

`4 sqrt(3)` sq. units

C

`6 sqrt(3)` sq. units

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
1

The circles are with centers (2,0) and `(-2,0)` and radius 4.
Therefore, the y-axis is their common chord.
`Delta ABC` is equilateral. Hence,
Area of ADBC `=(2xxsqrt(3))/(4)(4)^(2)=8sqrt(3)`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CENGAGE PUBLICATION|Exercise Multiple Correct Anser Type|29 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type (For Problem 1-3)|3 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 4.17|2 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

A rhombus is inscribed in the region common to the two circles x^2+y^2-4x-12=0 and x^2+y^2+4x-12=0 with two of its vertices on the line joining the centers of the circles. The are of the rhombus is (A) 8sqrt(3) sq.units (B) 4sqrt(3) sq.units (C) 6sqrt(3) sq.units (D) none of these

The area of the loop of the curve a y^2=x^2(a-x) is 4a^2s qdotu n i t s (b) (8a^2)/(15)s qdotu n i t s (16 a^2)/9s qdotu n i t s (d) None of these

Area bounded by the curve x y^2=a^2(a-x) and the y-axis is (pia^2)/2s qdotu n i t s (b) pia^2s qdotu n i t s 3pia^2s qdotu n i t s (d) None of these

The area enclosed between the curves y=(log)_e(x+e),x=(log)_e(1/y), and the x-axis is (a) 2s qdotu n i t s (b) 1s qdotu n i t s (c) 4s qdotu n i t s (d) none of these

Find the equation of the common chord of the two circles x^(2)+y^(2)-4x - 10y - 7 = 0 and 2x^(2) + 2y^(2) - 5x + 3y + 2 = 0 . Show that this chord is perpendicular to the line joining the centres of the two circles.

The area bounded by the curve a^2y=x^2(x+a) and the x-axis is (a^2)/3s qdotu n i t s (b) (a^2)/4s qdotu n i t s (3a^2)/4s qdotu n i t s (d) (a^2)/(12)s qdotu n i t s

The straight lines 7x-2y+10=0 and 7x+2y-10=0 form an isosceles triangle with the line y=2. The area of this triangle is equal to(a) (15)/7s qdotu n i t s (b) (10)/7s qdotu n i t s (c)(18)/7s qdotu n i t s (d) none of these

The graph of y^2+2x y+40|x|=400 divides the plane into regions. Then the area of the bounded region is (a) 200s qdotu n i t s (b) 400s qdotu n i t s (c) 800s qdotu n i t s (d) 500s qdotu n i t s

The number of common tangent(s) to the circles x^2+y^2+2x+8y-23=0 and x^2+y^2-4x-10 y-19=0 is 1 (b) 2 (c) 3 (d) 4

Center of the circle x^(2) + y^(2) - 4x + 6y - 12 = 0 is -

CENGAGE PUBLICATION-CIRCLE -Excercises (Single Correct Answer Type)
  1. The radius of the circle which has normals xy-2x-y+2= 0 and a tangent ...

    Text Solution

    |

  2. In triangle A B C , the equation of side B C is x-y=0. The circumcente...

    Text Solution

    |

  3. A rhombus is inscribed in the region common to the two circles x^2+y^2...

    Text Solution

    |

  4. The locus of the center of the circle such that the point (2, 3) is ...

    Text Solution

    |

  5. Consider a family of circles which are passing through the point (-1,1...

    Text Solution

    |

  6. The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the...

    Text Solution

    |

  7. A right angled isosceles triangle is inscribed in the circle x^2 + y^2...

    Text Solution

    |

  8. f(x , y)=x^2+y^2+2a x+2b y+c=0 represents a circle. If f(x ,0)=0 has e...

    Text Solution

    |

  9. The equation of the circumcircle of an equilateral triangle is x^2+y^2...

    Text Solution

    |

  10. If it is possible to draw a triangle which circumscribes the circle (...

    Text Solution

    |

  11. The locus of the centre of the circle(xcos alpha + y sin alpha - a)^2 ...

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. A B C D is a square of unit area. A circle is tangent to two sides of ...

    Text Solution

    |

  14. A circle of constant radius a passes through the origin O and cuts the...

    Text Solution

    |

  15. The circle x^2+y^2=4 cuts the line joining the points A(1, 0) and B(3,...

    Text Solution

    |

  16. If a circle of radius R passes through the origin O and intersects the...

    Text Solution

    |

  17. (6, 0), (0, 6) and (7, 7) are the vertices of a triangle. The circle i...

    Text Solution

    |

  18. If O is the origin and O Pa n dO Q are the tangents from the origin to...

    Text Solution

    |

  19. about to only mathematics

    Text Solution

    |

  20. If the conics whose equations are S-=sin^2thetax^2+2h x y+cos^2thetay^...

    Text Solution

    |