The eccentricity of the conic represented by `2x^2+5xy+2y^2+11x-7y-4=0` is

Explanation

We have `2x^(2)+5xy+2y^(2)-11x-7y-4=0`
Comparing this with general second-degree equation i.e.,
`ax^(2)+by^(2)+2hxy+2gx+2fy+c=0,` we get
`a=2,b=2,c=-4, h=5//2,g=-11//2,f=-7//2`
Now, `Delta=|{:(a,h,g),(h,b,f),(g,f,c):}|`
`=|{:(" 2"," "5//2,-11//2),(" "5//2," 2",-7//2),(-11//2,-7//2," "-4):}|=(81)/(4)ne0`
Also, `h^(2)-ab=(5//2)^(2)-(2)(2)gt0`
So, given equation represents a hyperbola.