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JEE Main 201511 AprilOnline
Exam
JEE Main
Year
2015
Date
11 April
Mode
Online
Subject
Mathematics
Chapter
Circle

JEE Main 2015 · 11 April · Online · Mathematics · Circle

If the incentre of an equilateral triangle is (1, 1) and the...

If the incentre of an equilateral triangle is (1,1)\left(1, 1\right) and the equation of its one side is 3x+4y+3=03x + 4y + 3 = 0, then the equation of the circumcircle of this triangle is:If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is 3x + 4y + 3 = 0 , then the

Options

  1. Ax2+y2−2x−2y−2=0{x}^{2} + {y}^{2} - 2x - 2y - 2 = 0
  2. Bx2+y2−2x−2y+2=0{x}^{2} + {y}^{2} - 2x - 2y + 2 = 0
  3. Cx2+y2−2x−2y−7=0{x}^{2} + {y}^{2} - 2x - 2y - 7 = 0
  4. Dx2+y2−2x−2y−14=0{x}^{2} + {y}^{2} - 2x - 2y - 14 = 0

Correct answer

D. x2+y2−2x−2y−14=0{x}^{2} + {y}^{2} - 2x - 2y - 14 = 0

Step-by-step solution

If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is 3x + 4y + 3 = 0 , then the

3x+4y+3=03x + 4y + 3 = 0

Since, for equilateral triangle centroid in center and circumcenter is the same therefore length of AB=∣3(1)+4(1)+332+42∣AB = \left|\dfrac{3\left(1\right) + 4\left(1\right) + 3}{\sqrt{{3}^{2} + {4}^{2}}}\right|

=105=2= \dfrac{10}{5} = 2

R=2(AB)=4R = 2\left(AB\right) = 4

As centroid divide median in the ratio 2:12: 1

Centre of the circle would be \left(1, 1\right)<br/><br/><br /><br />∴AnswerisAnswer is{x}^{2} + {y}^{2} - 2x - 2y - 14 = 0

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