Equation of Hyperbola
Hyperbola

120689 The eccentricity of the hyperbola \(x^2-y^2=9\) is

1 less than 1
2 1
3 \(\sqrt{2}\)
4 None of these
Hyperbola

120690 The equation of the conic with focus at \((1,-1)\) directrix along \(x-y+1=0\) and with eccentricity \(\sqrt{2}\) is

1 \(x^2-y^2=1\)
2 \(x y=1\)
3 \(2 x y-4 x+4 y+1=0\)
4 \(2 x y+4 x-4 y-1=0\)
Hyperbola

120691 The combined equation of the asymptotes of the hyperbola \(2 x^2+5 x y+2 y^2+4 x+5 y=0\) is -

1 \(2 x^2+5 x y+2 y^2+4 x+5 y+2=0\)
2 \(2 x^2+5 x y+2 y^2+4 x+5 y-2=0\)
3 \(2 x^2+5 x y+2 y^2=0\)
4 None of these
Hyperbola

120692 The equation of the hyperbola with vertices \((3\), \(0),(-3,0)\) and semi-latus rectum 4 is given by:

1 \(4 x^2-3 y^2+36=0\)
2 \(4 x^2-3 y^2+12=0\)
3 \(4 x^2-3 y^2-36=0\)
4 \(4 x^2+3 y^2-25=0\)
Hyperbola

120685 The eccentricity of the hyperbola \(x^2-y^2=2004\) is

1 \(\sqrt{3}\)
2 2
3 \(2 \sqrt{2}\)
4 \(\sqrt{2}\)
Hyperbola

120689 The eccentricity of the hyperbola \(x^2-y^2=9\) is

1 less than 1
2 1
3 \(\sqrt{2}\)
4 None of these
Hyperbola

120690 The equation of the conic with focus at \((1,-1)\) directrix along \(x-y+1=0\) and with eccentricity \(\sqrt{2}\) is

1 \(x^2-y^2=1\)
2 \(x y=1\)
3 \(2 x y-4 x+4 y+1=0\)
4 \(2 x y+4 x-4 y-1=0\)
Hyperbola

120691 The combined equation of the asymptotes of the hyperbola \(2 x^2+5 x y+2 y^2+4 x+5 y=0\) is -

1 \(2 x^2+5 x y+2 y^2+4 x+5 y+2=0\)
2 \(2 x^2+5 x y+2 y^2+4 x+5 y-2=0\)
3 \(2 x^2+5 x y+2 y^2=0\)
4 None of these
Hyperbola

120692 The equation of the hyperbola with vertices \((3\), \(0),(-3,0)\) and semi-latus rectum 4 is given by:

1 \(4 x^2-3 y^2+36=0\)
2 \(4 x^2-3 y^2+12=0\)
3 \(4 x^2-3 y^2-36=0\)
4 \(4 x^2+3 y^2-25=0\)
Hyperbola

120685 The eccentricity of the hyperbola \(x^2-y^2=2004\) is

1 \(\sqrt{3}\)
2 2
3 \(2 \sqrt{2}\)
4 \(\sqrt{2}\)
Hyperbola

120689 The eccentricity of the hyperbola \(x^2-y^2=9\) is

1 less than 1
2 1
3 \(\sqrt{2}\)
4 None of these
Hyperbola

120690 The equation of the conic with focus at \((1,-1)\) directrix along \(x-y+1=0\) and with eccentricity \(\sqrt{2}\) is

1 \(x^2-y^2=1\)
2 \(x y=1\)
3 \(2 x y-4 x+4 y+1=0\)
4 \(2 x y+4 x-4 y-1=0\)
Hyperbola

120691 The combined equation of the asymptotes of the hyperbola \(2 x^2+5 x y+2 y^2+4 x+5 y=0\) is -

1 \(2 x^2+5 x y+2 y^2+4 x+5 y+2=0\)
2 \(2 x^2+5 x y+2 y^2+4 x+5 y-2=0\)
3 \(2 x^2+5 x y+2 y^2=0\)
4 None of these
Hyperbola

120692 The equation of the hyperbola with vertices \((3\), \(0),(-3,0)\) and semi-latus rectum 4 is given by:

1 \(4 x^2-3 y^2+36=0\)
2 \(4 x^2-3 y^2+12=0\)
3 \(4 x^2-3 y^2-36=0\)
4 \(4 x^2+3 y^2-25=0\)
Hyperbola

120685 The eccentricity of the hyperbola \(x^2-y^2=2004\) is

1 \(\sqrt{3}\)
2 2
3 \(2 \sqrt{2}\)
4 \(\sqrt{2}\)
Hyperbola

120689 The eccentricity of the hyperbola \(x^2-y^2=9\) is

1 less than 1
2 1
3 \(\sqrt{2}\)
4 None of these
Hyperbola

120690 The equation of the conic with focus at \((1,-1)\) directrix along \(x-y+1=0\) and with eccentricity \(\sqrt{2}\) is

1 \(x^2-y^2=1\)
2 \(x y=1\)
3 \(2 x y-4 x+4 y+1=0\)
4 \(2 x y+4 x-4 y-1=0\)
Hyperbola

120691 The combined equation of the asymptotes of the hyperbola \(2 x^2+5 x y+2 y^2+4 x+5 y=0\) is -

1 \(2 x^2+5 x y+2 y^2+4 x+5 y+2=0\)
2 \(2 x^2+5 x y+2 y^2+4 x+5 y-2=0\)
3 \(2 x^2+5 x y+2 y^2=0\)
4 None of these
Hyperbola

120692 The equation of the hyperbola with vertices \((3\), \(0),(-3,0)\) and semi-latus rectum 4 is given by:

1 \(4 x^2-3 y^2+36=0\)
2 \(4 x^2-3 y^2+12=0\)
3 \(4 x^2-3 y^2-36=0\)
4 \(4 x^2+3 y^2-25=0\)
Hyperbola

120685 The eccentricity of the hyperbola \(x^2-y^2=2004\) is

1 \(\sqrt{3}\)
2 2
3 \(2 \sqrt{2}\)
4 \(\sqrt{2}\)
Hyperbola

120689 The eccentricity of the hyperbola \(x^2-y^2=9\) is

1 less than 1
2 1
3 \(\sqrt{2}\)
4 None of these
Hyperbola

120690 The equation of the conic with focus at \((1,-1)\) directrix along \(x-y+1=0\) and with eccentricity \(\sqrt{2}\) is

1 \(x^2-y^2=1\)
2 \(x y=1\)
3 \(2 x y-4 x+4 y+1=0\)
4 \(2 x y+4 x-4 y-1=0\)
Hyperbola

120691 The combined equation of the asymptotes of the hyperbola \(2 x^2+5 x y+2 y^2+4 x+5 y=0\) is -

1 \(2 x^2+5 x y+2 y^2+4 x+5 y+2=0\)
2 \(2 x^2+5 x y+2 y^2+4 x+5 y-2=0\)
3 \(2 x^2+5 x y+2 y^2=0\)
4 None of these
Hyperbola

120692 The equation of the hyperbola with vertices \((3\), \(0),(-3,0)\) and semi-latus rectum 4 is given by:

1 \(4 x^2-3 y^2+36=0\)
2 \(4 x^2-3 y^2+12=0\)
3 \(4 x^2-3 y^2-36=0\)
4 \(4 x^2+3 y^2-25=0\)
Hyperbola

120685 The eccentricity of the hyperbola \(x^2-y^2=2004\) is

1 \(\sqrt{3}\)
2 2
3 \(2 \sqrt{2}\)
4 \(\sqrt{2}\)