Home
Class 12
MATHS
Find the asymptotes and axes of hyperbol...

Find the asymptotes and axes of hyperbola having equation `xy-3y-4x+7=0`.

Text Solution

Verified by Experts

The correct Answer is:
Asymptotes; `x-3=-, y-4=0`
Transverse axis: `x-y+1=0`
Conjugate axis: `x+y-7=0`
We have hyperbola `(x-3)(y-4)=5`
Clearly, equation of pair of asymptotes is `(x-3)(y-4)=0`.
Thus, asymptotes are `x-3=0` and `y-4=0.`
Centre of the hyperbola is (3, 4).
Since hyperbola is rectangular, axes are bisectros of asymptotes having slopes `pm1`.
Therefore, equation of transverse axis is `y-4=1(x-3)` or `x-y+1=0` and equation of conjugate axis is `x+y-7=0`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE|Exercise Exercise (Single)|68 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise (Multiple)|18 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise 7.5|5 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Question Bank|21 Videos

Similar Questions

Explore conceptually related problems

Find the asymptotes of the curve x y-3y-2x=0 .

Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+8y^2+14 x+22 y+7=0

Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+9y^2+14 x+22 y+7=0

The equation of the transvers and conjugate axes of a hyperbola are, respectively, x+2y-3=0 and 2x-y+4=0 , and their respective lengths are sqrt(2) and 2sqrt(3)dot The equation of the hyperbola is 2/5(x+2y-3)^2-3/5(2x-y+4)^2=1 2/5(x-y-4)^2-3/5(x+2y-3)^2=1 2(2x-y+4)^2-3(x+2y-3)^2=1 2(x+2y-3)^2-3(2x-y+4)^2=1

Find the equation of the hyperbola which has 3x-4y+7=0 and 4x+3y+1=0 as its asymptotes and which passes through the origin.

The vertices of Delta ABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). The equation of the pair of asymptotes is

The vertices of Delta ABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). The equation of the rectangular hyperbola is

The combined equation of the asymptotes of the hyperbola 2x^2+5x y+2y^2+4x+5y=0 is a. 2x^2+5x y+2y^2+4x+5y+2=0 b. 2x^2+5x y+2y^2+4x+5y-2=0 c. 2x^2+5x y+2y^2=0 d.none of these

Find the general solution of the following differential equation. xy'+y=x^(4)

Statement 1 : The asymptotes of hyperbolas 3x+4y=2 and 4x-3y=5 are the bisectors of the transvers and conjugate axes of the hyperbolas. Statement 2 : The transverse and conjugate axes of the hyperbolas are the bisectors of the asymptotes.

Home
Profile