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If `omega` is one of the angles between the normals to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` at the point whose eccentric angles are `theta` and `pi/2+theta` , then prove that `(2cotomega)/(sin2theta)=(e^2)/(sqrt(1-e^2))`

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ARIHANT MATHS-ELLIPSE-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If omega is one of the angles between the normals to the ellipse (x...

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  2. The muinimum area of the triangle formed by the tangent to (x^(2))/(a...

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  3. Find the equation of the common tangent in the 1st quadrant to the cir...

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  4. An ellipse has O B as the semi-minor axis, Fa n dF ' as its foci...

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  5. In an ellipse, the distances between its foci is 6 and minor axis is 8...

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  6. Let P(x1, y1) and Q(x2, y2), y1 < 0, y2 < 0, be the end points of the...

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  7. A focus of an ellipse is at the origin. The directrix is the line x =4...

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  8. The line passing through the extremity A of the major exis and extremi...

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  9. The normal at a point P on the ellipse x^2+4y^2=16 meets the x-axis at...

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  10. a triangle A B C with fixed base B C , the vertex A moves such that co...

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  11. The conic having parametric representation x=sqrt3((1-t^(2)/(1+t^(2)))...

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  12. The ellipse x^2+""4y^2=""4 is inscribed in a rectangle aligned with...

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  13. Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/...

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  14. Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/...

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  15. Tangents are drawn from the point P(3,4) to the ellipse (x^2)/(9)+(y^2...

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  16. Equation of the ellipse whose axes are the axes of coordinates and ...

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  17. The ellipse E1:(x^2)/9+(y^2)/4=1 is inscribed in a rectangle R whose s...

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  18. Statement 1: An equation of a common tangent to the parabola y^2=16...

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  19. An ellipse is drawn by taking a diameter of the circle (x""""1)^2+""y^...

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  20. the equation of the circle passing through the foci of the ellip...

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  21. A vertical line passing through the point (h, 0) intersects the ellips...

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