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The vertices of DeltaABC lie on a rectan...

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

A

`xy=2x+y-2`

B

`2xy=x+2y+5`

C

`xy=x+y+1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let the equation of the hyperbola be `xy-x-y+1+lambda=0`.
It passes through (3,2). Hence, `lambda=-2`.
So, the equation of hyperbola is
`xy=x+y+1`
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CENGAGE-HYPERBOLA-Exercise (Comprehension)
  1. Consider an ellipse x^2/a^2+y^2/b^2=1 Let a hyperbola is having its v...

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  2. Consider the ellipse E1, x^2/a^2+y^2/b^2=1,(a>b). An ellipse E2 passes...

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  3. Consider the hyperbola (X^(2))/(9)-(y^(2))/(a^(2))=1 and the circle x^...

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  4. Consider the hyperbola (X^(2))/(9)-(y^(2))/(a^(2))=1 and the circle x^...

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  5. Find fofof If the funtion f(x)=x+1

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  6. The locus of the foot of perpendicular from my focus of a hyperbola up...

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  7. The locus of the foot of perpendicular from my focus of a hyperbola up...

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  8. The locus of the foot of perpendicular from my focus of a hyperbola up...

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  9. Let P(x, y) is a variable point such that |sqrt((x-1)^2+(y-2)^2)-sqr...

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  10. Let P(x, y) is a variable point such that |sqrt((x-1)^2+(y-2)^2)-sqr...

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  11. Let P(x, y) be a variable point such that |sqrt((x-1)^(2)+(y-2)^(2))...

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  12. In a hyperbola, the portion of the tangent intercepted between the asy...

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  13. In a hyperbola, the portion of the tangent intercepted between the asy...

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  14. In a hyperbola, the portion of the tangent intercepted between the asy...

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  15. A point P moves such that sum of the slopes of the normals drawn from ...

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  16. Evaluate int(2)^(5)(x+[x])dx ,where [.] denotes the greatest integer f...

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  17. A point P moves such that the sum of the slopes of the normals drawn f...

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  18. The vertices of DeltaABC lie on a rectangular hyperbola such that the ...

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  19. The vertices of DeltaABC lie on a rectangular hyperbola such that the ...

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  20. The vertices of DeltaABC lie on a rectangular hyperbola such that the ...

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