120767 If \(p, q\) are the eccentricities of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and its conjugate hyperbola respectively, then the area of the square (in sq. units) formed by the points of intersections of the ellipse \(\frac{x^2}{p^2}+\frac{y^2}{q^2}=1\) and the pair of lines \(\mathbf{x}^2-\mathrm{y}^2=0\) is

120768 If the latus rectum of a hyperbola subtends an angle of \(120^{\circ}\) at its centre, then its eccentricity is

120769 The lines \(x \cos \alpha+y \sin \alpha=P, \alpha \in R\) are chords of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{36}=1\) and they subtend a right angle at the centre of the hyperbola. The locus of the poles of these lines with respect to the given hyperbola is

120770 The eccentricity of the hyperbola \(\frac{(x-3)^2}{9}-\frac{4(y-1)^2}{45}=1\) is equal to
#[Qdiff: Hard, QCat: Numerical Based, examname: Kerala CEE-2013], we get -, We know that,, Comparing the above equation of hyperbola with standard equation of hyperbola, \(a^2=9\), \(a=3\), \(\mathrm{e}^2=1+\frac{\mathrm{b}^2}{\mathrm{a}^2}\), \(\mathrm{e}^2=1+\frac{9}{9}=1+1=2\), \(\mathrm{e}=\sqrt{2}\), Distance between directories of hyperbola, \(=\frac{2 \mathrm{a}}{\mathrm{e}}=\frac{2 \times 3}{\sqrt{2}}\), \(=3 \sqrt{2}\), 1058. If the foci of the ellipse \(\frac{x^2}{25}+\frac{y^2}{b^2}=1\) and the hyperbola \(\frac{x^2}{144}-\frac{y^2}{25}=\frac{1}{13}\) coincide, then the value of \(b^2\) is,

120679 The foci of the hyperbola \(4 x^2-9 y^2-1=0\) are

120767 If \(p, q\) are the eccentricities of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and its conjugate hyperbola respectively, then the area of the square (in sq. units) formed by the points of intersections of the ellipse \(\frac{x^2}{p^2}+\frac{y^2}{q^2}=1\) and the pair of lines \(\mathbf{x}^2-\mathrm{y}^2=0\) is

120768 If the latus rectum of a hyperbola subtends an angle of \(120^{\circ}\) at its centre, then its eccentricity is

120769 The lines \(x \cos \alpha+y \sin \alpha=P, \alpha \in R\) are chords of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{36}=1\) and they subtend a right angle at the centre of the hyperbola. The locus of the poles of these lines with respect to the given hyperbola is

120770 The eccentricity of the hyperbola \(\frac{(x-3)^2}{9}-\frac{4(y-1)^2}{45}=1\) is equal to
#[Qdiff: Hard, QCat: Numerical Based, examname: Kerala CEE-2013], we get -, We know that,, Comparing the above equation of hyperbola with standard equation of hyperbola, \(a^2=9\), \(a=3\), \(\mathrm{e}^2=1+\frac{\mathrm{b}^2}{\mathrm{a}^2}\), \(\mathrm{e}^2=1+\frac{9}{9}=1+1=2\), \(\mathrm{e}=\sqrt{2}\), Distance between directories of hyperbola, \(=\frac{2 \mathrm{a}}{\mathrm{e}}=\frac{2 \times 3}{\sqrt{2}}\), \(=3 \sqrt{2}\), 1058. If the foci of the ellipse \(\frac{x^2}{25}+\frac{y^2}{b^2}=1\) and the hyperbola \(\frac{x^2}{144}-\frac{y^2}{25}=\frac{1}{13}\) coincide, then the value of \(b^2\) is,

120679 The foci of the hyperbola \(4 x^2-9 y^2-1=0\) are

120767 If \(p, q\) are the eccentricities of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and its conjugate hyperbola respectively, then the area of the square (in sq. units) formed by the points of intersections of the ellipse \(\frac{x^2}{p^2}+\frac{y^2}{q^2}=1\) and the pair of lines \(\mathbf{x}^2-\mathrm{y}^2=0\) is

120768 If the latus rectum of a hyperbola subtends an angle of \(120^{\circ}\) at its centre, then its eccentricity is

120769 The lines \(x \cos \alpha+y \sin \alpha=P, \alpha \in R\) are chords of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{36}=1\) and they subtend a right angle at the centre of the hyperbola. The locus of the poles of these lines with respect to the given hyperbola is

120770 The eccentricity of the hyperbola \(\frac{(x-3)^2}{9}-\frac{4(y-1)^2}{45}=1\) is equal to
#[Qdiff: Hard, QCat: Numerical Based, examname: Kerala CEE-2013], we get -, We know that,, Comparing the above equation of hyperbola with standard equation of hyperbola, \(a^2=9\), \(a=3\), \(\mathrm{e}^2=1+\frac{\mathrm{b}^2}{\mathrm{a}^2}\), \(\mathrm{e}^2=1+\frac{9}{9}=1+1=2\), \(\mathrm{e}=\sqrt{2}\), Distance between directories of hyperbola, \(=\frac{2 \mathrm{a}}{\mathrm{e}}=\frac{2 \times 3}{\sqrt{2}}\), \(=3 \sqrt{2}\), 1058. If the foci of the ellipse \(\frac{x^2}{25}+\frac{y^2}{b^2}=1\) and the hyperbola \(\frac{x^2}{144}-\frac{y^2}{25}=\frac{1}{13}\) coincide, then the value of \(b^2\) is,

120679 The foci of the hyperbola \(4 x^2-9 y^2-1=0\) are

120767 If \(p, q\) are the eccentricities of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and its conjugate hyperbola respectively, then the area of the square (in sq. units) formed by the points of intersections of the ellipse \(\frac{x^2}{p^2}+\frac{y^2}{q^2}=1\) and the pair of lines \(\mathbf{x}^2-\mathrm{y}^2=0\) is

120768 If the latus rectum of a hyperbola subtends an angle of \(120^{\circ}\) at its centre, then its eccentricity is

120769 The lines \(x \cos \alpha+y \sin \alpha=P, \alpha \in R\) are chords of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{36}=1\) and they subtend a right angle at the centre of the hyperbola. The locus of the poles of these lines with respect to the given hyperbola is

120770 The eccentricity of the hyperbola \(\frac{(x-3)^2}{9}-\frac{4(y-1)^2}{45}=1\) is equal to
#[Qdiff: Hard, QCat: Numerical Based, examname: Kerala CEE-2013], we get -, We know that,, Comparing the above equation of hyperbola with standard equation of hyperbola, \(a^2=9\), \(a=3\), \(\mathrm{e}^2=1+\frac{\mathrm{b}^2}{\mathrm{a}^2}\), \(\mathrm{e}^2=1+\frac{9}{9}=1+1=2\), \(\mathrm{e}=\sqrt{2}\), Distance between directories of hyperbola, \(=\frac{2 \mathrm{a}}{\mathrm{e}}=\frac{2 \times 3}{\sqrt{2}}\), \(=3 \sqrt{2}\), 1058. If the foci of the ellipse \(\frac{x^2}{25}+\frac{y^2}{b^2}=1\) and the hyperbola \(\frac{x^2}{144}-\frac{y^2}{25}=\frac{1}{13}\) coincide, then the value of \(b^2\) is,

120679 The foci of the hyperbola \(4 x^2-9 y^2-1=0\) are

120767 If \(p, q\) are the eccentricities of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and its conjugate hyperbola respectively, then the area of the square (in sq. units) formed by the points of intersections of the ellipse \(\frac{x^2}{p^2}+\frac{y^2}{q^2}=1\) and the pair of lines \(\mathbf{x}^2-\mathrm{y}^2=0\) is

120768 If the latus rectum of a hyperbola subtends an angle of \(120^{\circ}\) at its centre, then its eccentricity is

120769 The lines \(x \cos \alpha+y \sin \alpha=P, \alpha \in R\) are chords of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{36}=1\) and they subtend a right angle at the centre of the hyperbola. The locus of the poles of these lines with respect to the given hyperbola is

120770 The eccentricity of the hyperbola \(\frac{(x-3)^2}{9}-\frac{4(y-1)^2}{45}=1\) is equal to
#[Qdiff: Hard, QCat: Numerical Based, examname: Kerala CEE-2013], we get -, We know that,, Comparing the above equation of hyperbola with standard equation of hyperbola, \(a^2=9\), \(a=3\), \(\mathrm{e}^2=1+\frac{\mathrm{b}^2}{\mathrm{a}^2}\), \(\mathrm{e}^2=1+\frac{9}{9}=1+1=2\), \(\mathrm{e}=\sqrt{2}\), Distance between directories of hyperbola, \(=\frac{2 \mathrm{a}}{\mathrm{e}}=\frac{2 \times 3}{\sqrt{2}}\), \(=3 \sqrt{2}\), 1058. If the foci of the ellipse \(\frac{x^2}{25}+\frac{y^2}{b^2}=1\) and the hyperbola \(\frac{x^2}{144}-\frac{y^2}{25}=\frac{1}{13}\) coincide, then the value of \(b^2\) is,

120679 The foci of the hyperbola \(4 x^2-9 y^2-1=0\) are