If the equation of incircle of an equilateral triangle is `x^2+y^2+4x-6y+4=0` then equation of circum circle of the triangle is

Options

A. `x^(2) + y^(2) + 4x - 6y + 23=0`
B. `x^(2) + y^(2) - 4x + 6y - 23=0`
C. `x^(2) + y^(2) + 4x - 6y - 23=0`
D. `x^(2) + y^(2) - 4x - 6y - 23=0`

Answer

3

Explanation

Incentre `=(-2,3)`
Inradius `=sqrt(4+9-4)=3`
Triangle is equilateral
`therefore` incentre = circumcentre
`therefore` circumcentre = (-2,3)
in `DeltaOBD`
`rArr Sin 30^(@) =(OD)/(OB)`
`rArr (1)/(2) = (3)/(OB) rArr OB = 6`
`therefore` Equation of cicrumcircle is
`(x + 2)^(2) +(y-3)^(2) = 36`
`rArr x^(2) +y^(2)+ 4x-6y- 23=0`