The area of the triangle formed by joining the centres of the circles

x2 + y2 + 2x + 4y - 4 = 0,

x2 + y2 + 6x + 4y + 9 = 0,

and x2 + y2 - 4x - 4y + 2 = 0 is

  1. 4 sq. units
  2. 6 sq. units
  3. 8 sq. units
  4. 12 sq. units

Answer (Detailed Solution Below)

Option 1 : 4 sq. units
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वृत्त के लिए सामान्य समीकरण 

उस वृत्त की त्रिज्या = और

केंद्र =  

त्रिभुज का क्षेत्रफल:

शीर्ष  वाले त्रिभुज के क्षेत्रफल को निम्न द्वारा ज्ञात किया गया है:

गणना:

Given the equation of circle are

x2 + y2 + 2x + 4y - 4 = 0    ----(1)

x2 + y2 + 6x + 4y + 9 = 0    -----(2)

x2 + y2 - 4x - 4y + 2 = 0       ----(3)

We know that, center of circle

are 

Hence, the center of given circles are

A(-1, -2), B(-3, -2), C(2, 2)

Hence, the area of a triangle ABC is

Δ = 

Δ = [-1(-2 - 2) + 2(-3 - 2) + 1(-6 + 4)]

⇒ Δ = 4 sq. unit

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