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The center of a rectangular hyperbola li...

The center of a rectangular hyperbola lies on the line `y=2xdot` If one of the asymptotes is `x+y+c=0` , then the other asymptote is (a)`6x+3y-4c=0` (b) `3x+6y-5c=0` (c)`3x-3y-c=0` (d) none of these

A

`6x+3y-4c=0`

B

`3x+6y-5c=0`

C

`3x-6y-c=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
The asymptotes of a rectangular hyperbola are perpendicular to each other.
Given one asymptote
`x+y+c=0`
Let the other asymptote be
`x-y+lambda=0`
We also know that the asymptotes pass through the centre of the hyperbola. Therefore, the line `2x-y=0` and the asymptotes must be concurrent.
Thus, we have
`|(2,-1,0),(1,1,c),(1,-1,lambda)|=0`
`"or "lambda=-(c)/(3)`
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CENGAGE-HYPERBOLA-Exercise (Single)
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  3. For hyperbola whose center is at (1, 2) and the asymptotes are paralle...

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  6. about to only mathematics

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  8. From any point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , tangents a...

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  9. The combined equation of the asymptotes of the hyperbola 2x^2+5x y+2y^...

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  10. The asymptotes of the hyperbola x y=h x+k y are (a)x-k=0 and y-h=0 (b...

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  11. The center of a rectangular hyperbola lies on the line y=2xdot If one ...

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  12. The equation of a rectangular hyperbola whose asymptotes are x=3 and y...

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  13. If tangents O Q and O R are dawn to variable circles having radius r a...

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  14. Four points are such that the line joining any two points is perpen...

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  15. If S1a n dS2 are the foci of the hyperbola whose length of the transve...

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  16. Suppose the circle having equation x^2+y^2=3 intersects the rectangula...

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  17. The equation of the chord joining two points (x(1),y(1)) and (x(2),y(2...

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  18. The locus of the foot of the perpendicular from the center of the h...

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