120797 The value of \(m\) for which \(y=m x+6\) is a tangent to the hyperbola \(\frac{x^2}{100}-\frac{y^2}{49}=1\) is

120798 The locus of point of intersection of tangents at the ends of normal chord of the hyperbola \(x^2-\) \(\mathbf{y}^2=\mathbf{a}^2\) is

120799 Intersection of two perpendicular tangents to the hyperbola \(\frac{x^2}{4}-\frac{y^2}{2}=1\) lies on the circle \(\mathbf{x}^2+\mathbf{y}^2=\) \(\qquad\)

120800 Let \(P(3 \sec \theta, 2 \tan \theta)\) and \(Q(3 \sec \phi, 2 \tan \phi)\) be two points on \(\frac{x^2}{9}-\frac{y^2}{4}=1\) such that \(\theta+\phi=\) \(\frac{\pi}{2}, 0\lt \theta, \phi\lt \frac{\pi}{2}\). Then the ordinate of the point of intersection of the normals at \(P\) and \(Q\) is

120797 The value of \(m\) for which \(y=m x+6\) is a tangent to the hyperbola \(\frac{x^2}{100}-\frac{y^2}{49}=1\) is

120798 The locus of point of intersection of tangents at the ends of normal chord of the hyperbola \(x^2-\) \(\mathbf{y}^2=\mathbf{a}^2\) is

120799 Intersection of two perpendicular tangents to the hyperbola \(\frac{x^2}{4}-\frac{y^2}{2}=1\) lies on the circle \(\mathbf{x}^2+\mathbf{y}^2=\) \(\qquad\)

120800 Let \(P(3 \sec \theta, 2 \tan \theta)\) and \(Q(3 \sec \phi, 2 \tan \phi)\) be two points on \(\frac{x^2}{9}-\frac{y^2}{4}=1\) such that \(\theta+\phi=\) \(\frac{\pi}{2}, 0\lt \theta, \phi\lt \frac{\pi}{2}\). Then the ordinate of the point of intersection of the normals at \(P\) and \(Q\) is

120797 The value of \(m\) for which \(y=m x+6\) is a tangent to the hyperbola \(\frac{x^2}{100}-\frac{y^2}{49}=1\) is

120798 The locus of point of intersection of tangents at the ends of normal chord of the hyperbola \(x^2-\) \(\mathbf{y}^2=\mathbf{a}^2\) is

120799 Intersection of two perpendicular tangents to the hyperbola \(\frac{x^2}{4}-\frac{y^2}{2}=1\) lies on the circle \(\mathbf{x}^2+\mathbf{y}^2=\) \(\qquad\)

120800 Let \(P(3 \sec \theta, 2 \tan \theta)\) and \(Q(3 \sec \phi, 2 \tan \phi)\) be two points on \(\frac{x^2}{9}-\frac{y^2}{4}=1\) such that \(\theta+\phi=\) \(\frac{\pi}{2}, 0\lt \theta, \phi\lt \frac{\pi}{2}\). Then the ordinate of the point of intersection of the normals at \(P\) and \(Q\) is

120797 The value of \(m\) for which \(y=m x+6\) is a tangent to the hyperbola \(\frac{x^2}{100}-\frac{y^2}{49}=1\) is

120798 The locus of point of intersection of tangents at the ends of normal chord of the hyperbola \(x^2-\) \(\mathbf{y}^2=\mathbf{a}^2\) is

120799 Intersection of two perpendicular tangents to the hyperbola \(\frac{x^2}{4}-\frac{y^2}{2}=1\) lies on the circle \(\mathbf{x}^2+\mathbf{y}^2=\) \(\qquad\)

120800 Let \(P(3 \sec \theta, 2 \tan \theta)\) and \(Q(3 \sec \phi, 2 \tan \phi)\) be two points on \(\frac{x^2}{9}-\frac{y^2}{4}=1\) such that \(\theta+\phi=\) \(\frac{\pi}{2}, 0\lt \theta, \phi\lt \frac{\pi}{2}\). Then the ordinate of the point of intersection of the normals at \(P\) and \(Q\) is