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Show that for all values of t the point x = a. `(1 + t^(2))/(1-t^(2)), y = (2at)/(1-t^(2))`lies on a fixed hyperbola. What is the value of the eccentricity of the hyperbola?

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The correct Answer is:
`e=sqrt(2)`
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CHHAYA PUBLICATION-HYPERBOLA-SHORT ANSWER TYPE QUESTIONS
  1. The hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 passes through the p...

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  2. Find the equation of the hyperbola whose eccentricity is(5)/(4), foc...

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  3. Find the equation of the hyperbola whose eccentricity is (5)/(4), f...

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  4. Find the equation of the hyperbola whose eccentricity is sqrt(3), fo...

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  5. Find the equation of the hyperbola whose eccentricity is sqrt(2), fo...

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  6. Find the equation of the hyperbola whose eccentricity is sqrt(2), fo...

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  7. Find the equation of the hyperbola whose eccentricity is 3, focus is...

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  8. Find the equation of the hyperbola, referred to its axes as lines para...

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  9. The distance between the vertices of a hyperbola is half the distance ...

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  10. The coordinates of the foci of a hyperbola are (16,0) and (-8,0) and i...

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  11. The centre of a hyperbola is at (2,4), the coordinates of one of its v...

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  12. Find the equation of the hyperbola centre at the origin, transeverse a...

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  13. The lengths of transverse and conjugate axes of a hyperbola are 4 unit...

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  14. e(1) and e(2) are respectively the eccentricites of a hyperbola and it...

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  15. Find the eccentricity of the hyperbola x^(2) - y^(2) = 1. If S, S(1) a...

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  16. P is a veriable poin on the hyperbola x^(2) - y^(2) =16 and A (8,0) is...

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  17. Show that the difference of focal distances of any point of the hyperb...

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  18. The coordinates of the foci of a hyperbola are (0,4) and (0,-4) and th...

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  19. Show that for all values of t the point x = a. (1 + t^(2))/(1-t^(2)), ...

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  20. Show that x =3(cotmu + tanmu), y =4(cotmu - tanmu) where mu is a veria...

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