Area of the equilateral `triangle` inscribed in the circle `x^(2) + y^(2) - 7x + 9y + 5 = 0`, is …………

Options

A. `(155)/(8)sqrt3sq` units
B. `(165)/(8)sqrt3` sq units
C. `(175)/(8)sqrt3` sq
D. `(165)/(8)sqrt3` sq units

Answer

B

Explanation

Given, `x^(2)+y^(2)-7x+9y+5=0`
`therefore R=sqrt((-7/2)^(2)+(9/2)^(2)-5)`
`=sqrt(49/4+81/4-5)=sqrt(110/2` in `DeltaOAB, cos 30^(0)=ab/R`
`rArr" "sqrt3/2=a_b/sqrt110_2`
`sqrt330/2=AB`
AC `=sqrt330/2=a :.` Area of equilateral triangle `=sqrt3/4(a)^(2)` ,
`=sqrt3/4xx330/4=(165sqrt3)/(8)` sq units