If the area of an equilateral triangle inscribed in the circle x 2 + y 2 + 10 x + 12 y + c = 0 is 27 3 sq . units , then c is equal to:

Step-by-step solution

Given, area of the equilateral triangle inscribed in the circle is 27 3 , hence 3 4   a 2 = 27   3 ⇒ a = 6 3   . . . 1 Again, r cos 30 ° = a 2 ⇒ r = 6 Hence, the radius of a circle, 5 2 + 6 2 - c = 6 ⇒ 25 + 36 - c = 36 ⇒ c = 25