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Let P(x, y) be a variable point such tha...

Let P(x, y) be a variable point such that
`|sqrt((x-1)^(2)+(y-2)^(2))-sqrt((x-5)^(2)+(y-5)^(2))|=3`
which represents a hyperbola.
The eccentricity e' of the corresponding conjugate hyperbola is

A

`tan^(-1)(4//3)`

B

`tan^(-1)(3//4)`

C

`tan^(-1)(5//3)`

D

`tan^(-1)(3//5)`

Text Solution

Verified by Experts

The correct Answer is:
B
The slope of the transverse axis is 3/4.
Therefore, the angle of rotation is
`theta=tan^(-1).(3)/(4)`
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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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