## Question

The centre of the hyperbola

### Solution

(2, 3)

The equation of the hyperbola is

Clearly, its centre is at (2, 3).

#### SIMILAR QUESTIONS

Find the locus of the poles of normal chords of the hyperbola

Find the condition for the lines *Ax*^{2} + 2*Hxy* + *By*^{2} = 0 to be conjugate diameters of .

Find the asymptotes of the hyperbola *xy* – 3*y* – 2*x* = 0.

A ray emanating from the point (5, 0) is incident on the hyperbola 9*x*^{2} – 16*y*^{2} = 144 at the point *P* with abscissa 8. Find the equation of the reflected ray after first reflection and point *P* lies in first quadrant.

The equations of the transverse and conjugate axes of a hyperbola are respectively 3*x* + 4*y* – 7 = 0, 4*x* – 3*y* + 8 = 0 and their respective lengths are 4 and 6. Find the equation of the hyperbola.

*A*, *B*, *C* are three points on the rectangular hyperbola *xy* = *c*^{2}, find

1. The area of the triangle *ABC*

2. The area of the triangle formed by the tangents at *A*, *B* and *C*.

Find the coordinates of the foci and the equation of the directrices of the rectangular hyperbola *xy* = *c*^{2}.

Find the equation of the hyperbola whose asymptotes are *x* + 2*y* + 3 = 0 and 3*x* + 4*y* + 5 = 0 and which passes through the point

(1,–1 ). Find also the equation of the conjugate of the conjugate hyperbola.

The vertices of the hyperbola

The eccentricity of the hyperbola with latusrectum 12 and semi-conjugate axis , is