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.

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Question

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.

None of these

diffcult

Solution

Correct option is

Combined equation of asymptotes is

Also we know that the equation of the hyperbola differs from that of asymptotes by a constant.

Let the equation of the hyperbola be

Since it passes through (1, –1) then

.

From (ii), equation of hyperbola is

But we know that equation of conjugate hyperbola

= 2(Combined equation of asymptotes) – (Equation of hyperbola)

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SIMILAR QUESTIONS

Q1

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

diffcult View solution

Q2

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

diffcult View solution

Q3

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

diffcult View solution

Q4

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

easy View solution

Q5

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

easy View solution

Q6

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.

medium View solution

Q7

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.

easy View solution

Q8

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.

diffcult View solution

Q9

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

medium View solution

Q10

The vertices of the hyperbola

easy View solution