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The equation of a rectangular hyperbola ...

The equation of a rectangular hyperbola whose asymptotes are `x=3` and `y=5` and passing through (7,8) is `x y-3y+5x+3=0` `x y+3y+4x+3=0` `x y-3y+5x-3=0` `x y-3y+5x+3=0`

A

`xy-3y+5x+3=0`

B

`xy+3y+4x+3=0`

C

`xy-3y+5x-3=0`

D

`xy-3y-5x+3=0`

Text Solution

Verified by Experts

The correct Answer is:
D
The equation of the rectangular hyperbola is
`(x-3)(y-5)+lambda=0`
It passes through (7, 8). Hence,
`4xx3+lambda or lambda=-12`
`therefore" "Xy-5x-3y+15-12=0`
`"or "xy-3y-5x+3=0`
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CENGAGE-HYPERBOLA-Exercise (Single)
  1. If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^...

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  2. Let any double ordinate P N P ' of the hyperbola (x^2)/(25)-(y^2)/(16)...

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  3. For hyperbola whose center is at (1, 2) and the asymptotes are paralle...

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  4. The asymptotes of the hyperbola (x^(2))/(a(1)^(2))-(y^(2))/(b(1)^(2))=...

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

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  6. If two distinct tangents can be drawn from the Point (alpha,2) on diff...

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  7. A hyperbola passes through (2,3) and has asymptotes 3x-4y+5=0 and 12 x...

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  8. From any point to the hyperbola ^2/a^2-y^2/b^2=1, tangents are drawn ...

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

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

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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 perpendic...

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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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  19. The curve xy = c(c > 0) and the circle x^2 +y^2=1 touch at two points,...

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  20. Let C be a curve which is the locus of the point of intersection of li...

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