Asymptote of Hyperbola
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Hyperbola

120826 The equation of a hyperbola whose asymptotes are \(3 x \pm 5 y=0\) and vertices are \(( \pm 5,0)\) is
#[Qdiff: Hard, QCat: Numerical Based, examname: Exp:D Given, [COMEDK-2012], Asymptotes are : \(3 x \pm 5 y=0\) and vertices are \(( \pm 5,0)\) We know that, standard equation of hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) \(5 y=3 x\) and \(5 y=-3 x\) \(y=\frac{3}{5} x\) and \(y=-\left(\frac{3}{5}\right) x\) \(\therefore \quad a=5\) and \(b=3\) So, equation of hyperbola \(\quad \frac{x^2}{25}-\frac{y^2}{9}=1\) \(9 x^2-25 y^2=225\), 1121. The angle between two asymptotes of the hyperbola \(\frac{x^2}{25}-\frac{y^2}{16}=1\),

1 \(3 \mathrm{x}^2-5 \mathrm{y}^2=25\)
2 \(5 x^2-3 y^2=225\)
3 \(25 \mathrm{x}^2-9 \mathrm{y}^2=225\)
4 \(9 x^2-25 y^2=225\)
Exp:D Given
Hyperbola

120827 The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is

1 \(y \cdot \frac{d y}{d x}=x\)
2 \(x \frac{d y}{d x}=-y\)
3 \(x \frac{d y}{d x}=y\)
4 \(x d y+y d x=c\)
VITEEE-2014
Hyperbola

120828 If the product of the lengths of the perpendiculars from any point on the hyperbola \(16 x^2-25 y^2=400\) to its asymptotes is \(p\) and the angle between the two asymptotes is \(\theta\), then \(p \tan \frac{\theta}{2}=\)

1 \(\frac{400}{41}\)
2 \(\frac{320}{41}\)
3 \(\frac{4}{5}\)
4 \(\frac{25}{16}\)
AP EAMCET-22.04.2018
Hyperbola

120829 The angle between the asymptotes of the hyperbola \(x^2-3 y^2=3\) is

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
AP EAMCET-2011
Hyperbola

120830 The equation of the hyperbola which passes through, the point, \((2,3)\) and has the asymptotes \(4 x+3 y-7=0\) and \(x-2 y-1=0\) is.

1 \(4 x^2+5 x y-6 y^2-11 x+11 y+50=0\)
2 \(4 x^2+5 x y-6 y^2-11 x+11 y-43=0\)
3 \(4 x^2-5 x y-6 y^2-11 x+11 y+57=0\)
4 \(4 x^2-5 x y-y^2-11 x+11 y-43=0\)
AP EAMCET-2010
NEET DIGITAL LIBRARY
Hyperbola

120826 The equation of a hyperbola whose asymptotes are \(3 x \pm 5 y=0\) and vertices are \(( \pm 5,0)\) is
#[Qdiff: Hard, QCat: Numerical Based, examname: Exp:D Given, [COMEDK-2012], Asymptotes are : \(3 x \pm 5 y=0\) and vertices are \(( \pm 5,0)\) We know that, standard equation of hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) \(5 y=3 x\) and \(5 y=-3 x\) \(y=\frac{3}{5} x\) and \(y=-\left(\frac{3}{5}\right) x\) \(\therefore \quad a=5\) and \(b=3\) So, equation of hyperbola \(\quad \frac{x^2}{25}-\frac{y^2}{9}=1\) \(9 x^2-25 y^2=225\), 1121. The angle between two asymptotes of the hyperbola \(\frac{x^2}{25}-\frac{y^2}{16}=1\),

1 \(3 \mathrm{x}^2-5 \mathrm{y}^2=25\)
2 \(5 x^2-3 y^2=225\)
3 \(25 \mathrm{x}^2-9 \mathrm{y}^2=225\)
4 \(9 x^2-25 y^2=225\)
Exp:D Given
Hyperbola

120827 The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is

1 \(y \cdot \frac{d y}{d x}=x\)
2 \(x \frac{d y}{d x}=-y\)
3 \(x \frac{d y}{d x}=y\)
4 \(x d y+y d x=c\)
VITEEE-2014
Hyperbola

120828 If the product of the lengths of the perpendiculars from any point on the hyperbola \(16 x^2-25 y^2=400\) to its asymptotes is \(p\) and the angle between the two asymptotes is \(\theta\), then \(p \tan \frac{\theta}{2}=\)

1 \(\frac{400}{41}\)
2 \(\frac{320}{41}\)
3 \(\frac{4}{5}\)
4 \(\frac{25}{16}\)
AP EAMCET-22.04.2018
Hyperbola

120829 The angle between the asymptotes of the hyperbola \(x^2-3 y^2=3\) is

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
AP EAMCET-2011
Hyperbola

120830 The equation of the hyperbola which passes through, the point, \((2,3)\) and has the asymptotes \(4 x+3 y-7=0\) and \(x-2 y-1=0\) is.

1 \(4 x^2+5 x y-6 y^2-11 x+11 y+50=0\)
2 \(4 x^2+5 x y-6 y^2-11 x+11 y-43=0\)
3 \(4 x^2-5 x y-6 y^2-11 x+11 y+57=0\)
4 \(4 x^2-5 x y-y^2-11 x+11 y-43=0\)
AP EAMCET-2010
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Hyperbola

120826 The equation of a hyperbola whose asymptotes are \(3 x \pm 5 y=0\) and vertices are \(( \pm 5,0)\) is
#[Qdiff: Hard, QCat: Numerical Based, examname: Exp:D Given, [COMEDK-2012], Asymptotes are : \(3 x \pm 5 y=0\) and vertices are \(( \pm 5,0)\) We know that, standard equation of hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) \(5 y=3 x\) and \(5 y=-3 x\) \(y=\frac{3}{5} x\) and \(y=-\left(\frac{3}{5}\right) x\) \(\therefore \quad a=5\) and \(b=3\) So, equation of hyperbola \(\quad \frac{x^2}{25}-\frac{y^2}{9}=1\) \(9 x^2-25 y^2=225\), 1121. The angle between two asymptotes of the hyperbola \(\frac{x^2}{25}-\frac{y^2}{16}=1\),

1 \(3 \mathrm{x}^2-5 \mathrm{y}^2=25\)
2 \(5 x^2-3 y^2=225\)
3 \(25 \mathrm{x}^2-9 \mathrm{y}^2=225\)
4 \(9 x^2-25 y^2=225\)
Exp:D Given
Hyperbola

120827 The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is

1 \(y \cdot \frac{d y}{d x}=x\)
2 \(x \frac{d y}{d x}=-y\)
3 \(x \frac{d y}{d x}=y\)
4 \(x d y+y d x=c\)
VITEEE-2014
Hyperbola

120828 If the product of the lengths of the perpendiculars from any point on the hyperbola \(16 x^2-25 y^2=400\) to its asymptotes is \(p\) and the angle between the two asymptotes is \(\theta\), then \(p \tan \frac{\theta}{2}=\)

1 \(\frac{400}{41}\)
2 \(\frac{320}{41}\)
3 \(\frac{4}{5}\)
4 \(\frac{25}{16}\)
AP EAMCET-22.04.2018
Hyperbola

120829 The angle between the asymptotes of the hyperbola \(x^2-3 y^2=3\) is

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
AP EAMCET-2011
Hyperbola

120830 The equation of the hyperbola which passes through, the point, \((2,3)\) and has the asymptotes \(4 x+3 y-7=0\) and \(x-2 y-1=0\) is.

1 \(4 x^2+5 x y-6 y^2-11 x+11 y+50=0\)
2 \(4 x^2+5 x y-6 y^2-11 x+11 y-43=0\)
3 \(4 x^2-5 x y-6 y^2-11 x+11 y+57=0\)
4 \(4 x^2-5 x y-y^2-11 x+11 y-43=0\)
AP EAMCET-2010
For More Updates join with Us
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Hyperbola

120826 The equation of a hyperbola whose asymptotes are \(3 x \pm 5 y=0\) and vertices are \(( \pm 5,0)\) is
#[Qdiff: Hard, QCat: Numerical Based, examname: Exp:D Given, [COMEDK-2012], Asymptotes are : \(3 x \pm 5 y=0\) and vertices are \(( \pm 5,0)\) We know that, standard equation of hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) \(5 y=3 x\) and \(5 y=-3 x\) \(y=\frac{3}{5} x\) and \(y=-\left(\frac{3}{5}\right) x\) \(\therefore \quad a=5\) and \(b=3\) So, equation of hyperbola \(\quad \frac{x^2}{25}-\frac{y^2}{9}=1\) \(9 x^2-25 y^2=225\), 1121. The angle between two asymptotes of the hyperbola \(\frac{x^2}{25}-\frac{y^2}{16}=1\),

1 \(3 \mathrm{x}^2-5 \mathrm{y}^2=25\)
2 \(5 x^2-3 y^2=225\)
3 \(25 \mathrm{x}^2-9 \mathrm{y}^2=225\)
4 \(9 x^2-25 y^2=225\)
Exp:D Given
Hyperbola

120827 The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is

1 \(y \cdot \frac{d y}{d x}=x\)
2 \(x \frac{d y}{d x}=-y\)
3 \(x \frac{d y}{d x}=y\)
4 \(x d y+y d x=c\)
VITEEE-2014
Hyperbola

120828 If the product of the lengths of the perpendiculars from any point on the hyperbola \(16 x^2-25 y^2=400\) to its asymptotes is \(p\) and the angle between the two asymptotes is \(\theta\), then \(p \tan \frac{\theta}{2}=\)

1 \(\frac{400}{41}\)
2 \(\frac{320}{41}\)
3 \(\frac{4}{5}\)
4 \(\frac{25}{16}\)
AP EAMCET-22.04.2018
Hyperbola

120829 The angle between the asymptotes of the hyperbola \(x^2-3 y^2=3\) is

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
AP EAMCET-2011
Hyperbola

120830 The equation of the hyperbola which passes through, the point, \((2,3)\) and has the asymptotes \(4 x+3 y-7=0\) and \(x-2 y-1=0\) is.

1 \(4 x^2+5 x y-6 y^2-11 x+11 y+50=0\)
2 \(4 x^2+5 x y-6 y^2-11 x+11 y-43=0\)
3 \(4 x^2-5 x y-6 y^2-11 x+11 y+57=0\)
4 \(4 x^2-5 x y-y^2-11 x+11 y-43=0\)
AP EAMCET-2010
NEET DIGITAL LIBRARY
Hyperbola

120826 The equation of a hyperbola whose asymptotes are \(3 x \pm 5 y=0\) and vertices are \(( \pm 5,0)\) is
#[Qdiff: Hard, QCat: Numerical Based, examname: Exp:D Given, [COMEDK-2012], Asymptotes are : \(3 x \pm 5 y=0\) and vertices are \(( \pm 5,0)\) We know that, standard equation of hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) \(5 y=3 x\) and \(5 y=-3 x\) \(y=\frac{3}{5} x\) and \(y=-\left(\frac{3}{5}\right) x\) \(\therefore \quad a=5\) and \(b=3\) So, equation of hyperbola \(\quad \frac{x^2}{25}-\frac{y^2}{9}=1\) \(9 x^2-25 y^2=225\), 1121. The angle between two asymptotes of the hyperbola \(\frac{x^2}{25}-\frac{y^2}{16}=1\),

1 \(3 \mathrm{x}^2-5 \mathrm{y}^2=25\)
2 \(5 x^2-3 y^2=225\)
3 \(25 \mathrm{x}^2-9 \mathrm{y}^2=225\)
4 \(9 x^2-25 y^2=225\)
Exp:D Given
Hyperbola

120827 The differential equation of the rectangular hyperbola, where axes are the asymptotes of the hyperbola, is

1 \(y \cdot \frac{d y}{d x}=x\)
2 \(x \frac{d y}{d x}=-y\)
3 \(x \frac{d y}{d x}=y\)
4 \(x d y+y d x=c\)
VITEEE-2014
Hyperbola

120828 If the product of the lengths of the perpendiculars from any point on the hyperbola \(16 x^2-25 y^2=400\) to its asymptotes is \(p\) and the angle between the two asymptotes is \(\theta\), then \(p \tan \frac{\theta}{2}=\)

1 \(\frac{400}{41}\)
2 \(\frac{320}{41}\)
3 \(\frac{4}{5}\)
4 \(\frac{25}{16}\)
AP EAMCET-22.04.2018
Hyperbola

120829 The angle between the asymptotes of the hyperbola \(x^2-3 y^2=3\) is

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
AP EAMCET-2011
Hyperbola

120830 The equation of the hyperbola which passes through, the point, \((2,3)\) and has the asymptotes \(4 x+3 y-7=0\) and \(x-2 y-1=0\) is.

1 \(4 x^2+5 x y-6 y^2-11 x+11 y+50=0\)
2 \(4 x^2+5 x y-6 y^2-11 x+11 y-43=0\)
3 \(4 x^2-5 x y-6 y^2-11 x+11 y+57=0\)
4 \(4 x^2-5 x y-y^2-11 x+11 y-43=0\)
AP EAMCET-2010