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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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Assertion (A): The locus of the point ((e^(2t)+e^(-2t))/(2), (e^(2t)-e^(-2t))/(2)) when 't' is a parameter represents a rectangular hyperbola. Reason (R ) : The eccentricity of a rectangular hyperbola is 2.

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If e_(1) is the eccentricity of the ellipse x^(2)/16+y^(2)/25=1 and e_(2) is the eccentricity of a hyperbola passing through the foci of the given ellipse and e_(1)e_(2)=1 , then the equation of such a hyperbola among the following is

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AAKASH SERIES-HYPERBOLA-Exercise -I
  1. The eccentricity of the conjugate hyperbola of the hyperola x^(2)-3y^(...

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  2. If e(1) and e(2) are eccentricities of the hyperbolas xy=c^(2) and x^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 distance between the foci is 4sqrt(13) and the length of conjugate...

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  5. The latus rectum of a hyperbola (x^(2))/( 16) -(y^(2))/( p) =1 is 4(1...

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  6. If the latus rectum through one focum subtends a right angle at the fa...

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  7. If the lactus recturm of a hyperbola through one focus subtends 60^@ a...

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  8. If the latus rectum of a hyperola forms an equilateral triangle with t...

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  9. The line y=mx+2 touches the hyperola 4x^(2)-9y^(2)=36 then m=

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  10. Equations of tangents to the hyperbola 4x^(2)-3y^(2)=24 which makes an...

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  11. The equation of the tangents to the hyperbola 3x^(2) -4y^(2) =12 whic...

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  12. The point of contact of 9x+8y-11=0 to the hyperbola 3x^(2)-4y^(2)=11 i...

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  13. The nummber of tangents to x^(2)//9-y^(2)//4=1 throught (6,2) is

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  14. For all real values of m' the straight line y=mx + sqrt(9m^(2)-4) is a...

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  15. The condition that the line x=my+c may be a tangent of x^(2)/a^(2)-y^(...

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  16. Product of perpendiculars from the foci of x^(2)/4-y^(2)/9=1" to "y=mx...

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  17. If m1, m2, are slopes of the tangens to the hyperbola x^(2)//25-y^(2)/...

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  18. Number of points from where perpendicular tangents can be drawn to the...

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  19. The equation of the auxiliary circle of x^(2)/(16)-y^(2)/(25)=1 is

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  20. Locus of feet of perpendicular from (5,0) to the tangents of (x^(2))/(...

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