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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`

A

`2(x+2y-3)^(2)-3(2x-y+4)^(2)=5`

B

`2(2x-y+4)^(2)-3(x+2y-3)^(2)=5`

C

`2(x+2y-3)^(2)-3(2x-y+4)^(2)=1`

D

`2(2x-y+4)^(2)-3(x+2y-3)^(2)=1`

Text Solution

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The correct Answer is:
B
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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) .The equation of the hyperbola is (2)/(5)(x+2y-3)^(2)-(3)/(5)(2x-y+4)^(2)=1(2)/(5)(x-y-3)^(2)-3(x+2y-3)^(2)=12(x+2y-3)^(2)-3(2x-y+4)^(2)=1

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ARIHANT MATHS-HYPERBOLA-Exercise For Session 3
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  8. If the sum of the slopes of the normal from a point P to the hyperbola...

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  9. If S=0 is the equation of the hyperbola x^2+4x y+3y^2-4x+2y+1=0 , then...

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  12. The equation of the transvers and conjugate axes of a hyperbola are, ...

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  15. The asymptotes of a hyperbola are parallel to lines 2x+3y=0 and 3x+2y=...

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