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If any two chords be drawn through two points on the major axis of the ellipse `x^2/a^2+y^2/b^2=1` equidistant from the centre prove that `tan""alpha/2 tan""beta/2 tan""gamma/2=1` where `alpha,beta,gamma,delta` are the eccentricity angles of the extremities of the chord.

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AAKASH SERIES-ELLIPSE-PRACTICE EXERCISE
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  2. If length of the major axis is 8 and e = 1/sqrt(2)Axes are co-ordinate...

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  3. The equation of the ellipse whose vertices are (2, 5), (2, -1) and ecc...

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  4. The equation of the ellipse whose focus is (2, 4), centre is (3, 4) an...

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  5. The equation of the ellipse whose centre is (5, 2) vertex is (9, 2), t...

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  6. Axes are co-ordinate axes, the ellipse passes through the points where...

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  7. Axes are co-ordinate axes, A and B are ends of major axes and minor ax...

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  8. The axis of the ellipse are coordinate axes. It passes through the pts...

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  9. Latus Rectum is 4 and e=(1)/sqrt(2) axes are co­ordinate axes, eq. ...

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  10. The equation of the ellipse with its axes as the coordinate axes and ...

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  11. The centre of a ellipse where axes is parllel to co-ordinate axes is (...

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  12. The equation of the ellipse whose vertices are (-4, 1), (6, 1) and one...

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  13. If the equation (x^(2))/(9-k)+(y^(2))/(5-k)=1 represents an ellipse t...

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  14. The centre of the ellipse 4x^(2)+9y^(2)-24x+36y-72=0 is

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  15. The foci of the ellipse 36x^(2) + 9y^(2) = 324 are

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  16. The coordinates of the foci of the ellipse 4x^(2) + 9y^(2) = 1 are

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  17. The length of the latusrectum of ((x-3)^(2))/(16)+(y-2)^(2)/(36)=1 is

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  18. The equation of the minor axis of the ellipse (x-1)^(2)/(9)+(y-6)^(2)/...

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  19. The equations of the directrices of the ellipse 9x^(2) + 25y^(2) = 22...

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  20. The vertices of the ellipse 9x^(2) + 25y^(2) - 90x - 150y + 225 = 0 ar...

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  21. The foci of the ellipse 9x^(2)+ 5(y^(2)-10y +25)=45 are

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