﻿   A, B, C 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 A, B and C.  : Kaysons Education

# A, B, C 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 A, B and C.

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### 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.