Question

 

The vertices of the hyperbola

     

Solution

Correct option is

(6, 3) and (–2, 3)

 

The equation of the hyperbola is   

        

  

The coordinates of the vertices are given by 

        x – 2 = ±4, y – 3 = 0  

SIMILAR QUESTIONS

Q1

Find the locus of the mid-points of the chords of the hyperbola  which subtend a right angle at the origin.

Q2

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

Q3

Find the condition for the lines Ax2 + 2Hxy + By2 = 0 to be conjugate diameters of  .

Q4

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

Q5

A ray emanating from the point (5, 0) is incident on the hyperbola 9x2 – 16y2 = 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.  

Q6

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

Q7

 

ABC are three points on the rectangular hyperbola xy = c2, find

1. The area of the triangle ABC

2. The area of the triangle formed by the tangents at AB and C

Q8

Find the coordinates of the foci and the equation of the directrices of the rectangular hyperbola xy = c2.

Q9

 

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

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

Q10

 

The centre of the hyperbola