Hyperbola Questions (161)

If the length of the transverse and conjugate axes of a hyperbola be 8 and 6 respectively, then the difference focal distances of any point of the hyperbola will be:

The one which does not represent a hyperbola is:

If the circle x2 + y2 = k2 and the rectangular hyperbola xy = k have no points in common, then the number of integral values of k, is:

A hyperbola passes through the points (3, 2) and (-17, 12) and has its centre at origin and transverse axis is along x-axis. The length of its transverse axis is

Let \(H: \frac{-x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) be the hyperbola, whose eccentricity is \(\sqrt{3}\) and the length of the latus rectum is \(4 \sqrt{3}\). Suppose the point (\(\alpha, 6\)), \(\alpha \gt 0\) lies on \(H\). If \(\beta\) is the product of the focal distances of the point (\(\alpha, 6\)), then \(\alpha^{2}+\beta\) is equal to:

A tangent to the hyperbola x2 - 2y2 = 4 meets x-axis at P and y-axis at Q. Line PR and QR are drawn such that OPRQ is a rectangle (where O is the origin). The locus of is:

If the line \(y = mx + 7\sqrt{3}\) is normal to the hyperbola \(\dfrac{x^2}{24} - \dfrac{y^2}{18} = 1\), then a value of \(m\) is __________ (up to four decimal places).

If a hyperbola passes through the point P(10, 16) and it has vertices at (\(\pm\)6, 0), then the equation of the normal to it at P is:

The eccentricity of the hyperbola, whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is

The equation 16x2 - 3y2 - 32x + 12 y - 44 = 0 represents a hyperbola:

The distance between the directrices of a rectangular hyperbola is 10 units, then distance between its foci is