A cruve is respresented by `C=21x^(2)-6xy+29y^(2)+6x-58y-151=0`
The eccentricity of the cruve is

Options

A. `6,2 sqrt(6)`
B. `5,2sqrt(5)`
C. `4,4sqrt(5)`
D. none of these

Explanation

`24x^(2)-6xy+29y+6x-58y-151=0`
`2(x-3y+3)^(2)+2(3x+y-1)^(2)=180`
or `((x-3y+3)^(2))/(60)+((3x+y-1)^(2))/(90)=1`
or `((x-3y+3)/(sqrt(1+3^(2))sqrt(6)))^(2)+((3x+y-1)/(3sqrt(1+3^(2))))=1`
Thus, C is an ellipse whose lengths of axes are `6,2sqrt(6)`.
The minor and the major axes are `x-3y+3=0 and 3x+y-1=0`, respectively.
Their point of intersection gives the center of the center of the conic. Therefore, Center `-=(o,1)`