Question

 

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

Solution

Correct option is

 

Let coordinates of AB and C on the hyperbola xy = c2 are  respectively. 

1. Area of triangle ABC, 

       

       

       

       

2. equations of tangents at ABC are 

                  

            

  

  

where,  

              

  

From (i) 

       

       

SIMILAR QUESTIONS

Q1

Find the equation of the tangent to the hyperbola x2 – 4y2 = 36 which is perpendicular to the line x – y + 4 = 0.  

Q2

 

Find the equation and the length of the common tangents to hyperbola 

            

Q3

Find the locus of the foot of perpendicular from the centre upon any normal to the hyperbola .

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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.  

Q9

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.  

Q10

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