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The locus of the point ( (e^(t) +e^(-t))...

The locus of the point `( (e^(t) +e^(-t))/( 2),(e^t-e^(-t))/(2))` is a hyperbola of eccentricity

A

`sqrt3`

B

`3`

C

`sqrt2`

D

2

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-Hyperbola -EXERCISE 1A
  1. Let LL' be the latus rectum through the focus S of a hyperbola and A '...

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  2. The eccentricity of the hyperbola x= ( a)/(2) ( t+1//t), y=(a)/(2) (...

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  3. The locus of the point ( (e^(t) +e^(-t))/( 2),(e^t-e^(-t))/(2)) is a h...

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  4. The equation of directrices of the hyperbola 5x^(2) -4y^(2) -30x -8y ...

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  5. The equations of the latus recta of the hyperbola 9x^(2) -16y^(2) -18...

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  6. The equation of the conjugate axis of the hyperbola ((x-5)^(2))/(16) -...

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  7. The equation of transverse axis of the hyperbola 5x^(2) -4y^(2) -30x ...

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  8. The equation of the axes of the hyperbola 9x^(2) -16y^(2) +72x -32y -1...

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  9. The equation of the hyperbola whose eccentricity 2 and foci are the fo...

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  10. PN is the ordinate of any point P on the hyperbola x^(2)//a^(2) -y^(2...

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  11. If the foci of the ellips (x^(2))/( 25)+ ( y^(2))/( 16) =1 and the hy...

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  12. The foci of the ellips (x^(2))/( 16) +(y^(2))/( b^(2) ) =1 and the h...

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  13. For the hyperbola (x^(2))/( cos ^(2) alpha ) -(y^(2))/(sin^(2) alpha ...

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  14. A hyperbola passes through a focus of the ellips (x^(2))/(169) +(y^(2...

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  15. The equation of the tangent to the hyperbola 3x^(2) -2y^(2) =10 at(2,...

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  16. The equation of the normal to the hyperbola x^(2) -4y ^(2) =5 at (3,-...

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  17. The sum and product of the slopes of the tangents to the hyperbola 2x...

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  18. The condition that the line y = mx+c may be a tangent to the hyperbo...

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  19. The condition that the line x cos alpha + y sin alpha =p to be a tange...

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  20. The condition that the line (x)/(p) +(y)/( q) =1 to be a tangent to ...

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