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If the area of an equilateral triangle inscribed in the circle, x^2 + y^2 +10x +12 y +c = 0 is 27\sqrt3 sq.units then c is equal to:

  • Option 1)

    -25

  • Option 2)

    13

  • Option 3)

    25

  • Option 4)

    20

Answers (1)

best_answer

 

General form of a circle -

x^{2}+y^{2}+2gx+2fy+c= 0
 

- wherein

centre = \left ( -g,-f \right )

radius = \sqrt{g^{2}+f^{2}-c}

Equilateral triangle -

Centriod, circumcentre, orthocentre and incentre coincide.

From the concept

3(\frac{1}{2}r^{2}\sin 120^{\circ})=27\sqrt 3                                  

\frac{1}{2}r^{2}\cdot \frac{\sqrt3}{2}=\frac{27\sqrt 3}{3}

r^{2}=36

Radius=\sqrt{g^{2}+f^{2}-c}

\sqrt{36}=\sqrt{25+36-c}

c=25    

 

 


 

 


Option 1)

-25

Option 2)

13

Option 3)

25

Option 4)

20

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