﻿ Find the hyperbola whose asymptotes are 2x – y = 3 and 3x + y – 7 = 0 and which passes through the point (1, 1). : Kaysons Education

# Find The Hyperbola Whose Asymptotes Are 2x – Y = 3 And 3x + Y – 7 = 0 And Which Passes Through The Point (1, 1).

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## Question

### Solution

Correct option is

6

The equation of the hyperbola differs from the equation of the asymptotes by a constant.

The equation of the hyperbola with asymptotes 3x + y – 7 = 0

and 2x – y = 3 is

(3x + y – 7)(2x – y – 3) + k = 0

It passes through (1, 1)  k = – 6

Hence the equation of the hyperbola is

(3x + y – 7)(2x – y – 3) = 6

#### SIMILAR QUESTIONS

Q1

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Q2

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Q3

Find the equations of tangents to the hyperbola x2 – 4y = 36 which are perpendicular to the line x – y + 4 = 0

Q4

Find the coordinates of foci, the eccentricity and latus rectum. Determine also the equation of its directrices for the hyperbola

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Q5

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Q6

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Q7

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Q8

Find the equation of the triangles drawn from the point (–2, –1) to the hyperbola 2x2 – 3y2 = 6.

Q9

Find the range of ‘a’ for which two perpendicular tangents can be drawn to the hyperbola from any point outside the hyperbola

.

Q10

The locus of a variable point whose distance from (–2, 0) is  times its distance from the line , is