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Show that equations x = 5 * (1 - t^(2))...

Show that equations `x = 5 * (1 - t^(2))/(1 + t^(2)), y = 6 * (t)/(1 + t^(2) ) ` where t is a variable parameter, define an ellipse . Find its eccentricity .

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The correct Answer is:
`e = (4)/(5)`
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CHHAYA PUBLICATION-ELLIPSE-Short Answer Type Questios
  1. Find the equation of the ellipse whose eccentricity is (1)/(2) ...

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  2. Find the equation of the ellipse whose focus is (3, 4) , directr...

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  3. A point moves so that its distance from (0,-3) is (1)/(sqrt(2)) tim...

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  4. Find the equation of the ellipse whose major axis is parallel to x - a...

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  5. Find the equation of the ellipse whose major axis is parallel to x - a...

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  6. Find the equation of the ellipse, for which the foci are (0,1) and (0...

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  7. The eccentricity of an ellipse is (1)/(2) , focus is S (0,0) and the ...

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  8. The lengths of major and minor axes of an ellipse are 8 and 6 and thei...

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  9. Show that the point (2,(2)/(sqrt(5))) lies on the ellipse 4x^(2) +...

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  10. Prove that SP + S'P = 20 for the ellipse (x^(2))/(100) + (y^(2))/(36)...

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  11. If t be a variable parameter, show that the point x = a(1 -t^(2))/(1...

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  12. A point moves on a plane is such a manner that the sum of its istances...

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  13. Find the locus of the point , the ratio of whose distances from the li...

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  14. The lengths of the major and minor axes of an ellipse are 2 a and 2b ...

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  15. Show that for an ellipse the straight line joining the upper end of on...

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  16. Find the equation of the auxiliary circle of the ellipse 16x^(2)+25y^...

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  17. If the eccentric angles of the two points on the ellipse (x^(2))/(a^(2...

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  18. Show that equations x = 5 * (1 - t^(2))/(1 + t^(2)), y = 6 * (t)/(1 +...

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  19. Show tht the locus of the middle points of chords of the ellipse (x^(2...

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  20. If P(x , y) ,F(1) (3,0) , F(2) (-3, 0) " and " 16x^(2) + 25 y^(2) = 40...

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