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If the chord, joining two points whose e...

If the chord, joining two points whose eccentric angles are `alpha and beta`, cuts the major axis ofthe ellipse `x^2/a^2 + y^2/b^2=1` at a distance c fromn the centre, then `tan alpha//2.tan beta//2` is equal to

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If the chord,joining two points whose eccentric angles are alpha and beta, cuts the major axis ofthe ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at a distance crromn the centre,then tan alpha/2.tan beta/2 is equal to

If (alpha-beta)=(pi)/(2) ,then the chord joining the points whose eccentric angles are alpha and beta of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=(1)/(k) , then ( 5k^(2)+2) is equal to

IF alpha , beta are eccentric angles of end points of a focal chord of the ellipse x^(2)/a^(2) + y^(2)/b^(2) =1 then tan(alpha /2) tan (beta/2) is equal to

If a chord joining two points whose eccentric angles are alpha and beta so that tan alpha.tan beta=-(a^(2))/(b^(2)), subtend an angle theta at the centre of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then theta=

If (a sec alpha,b tan alpha) and (a sec beta ,b tan beta) be the ends of a chord of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passing through the focus (ae,0) then tan (alpha/2) tan (beta/2) is equal to

If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^(2))/(a^(2)))+((y^(2))/(b^(2)))=1 subtends a right angle at the vertex A(a,0), then prove that tan((a)/(2))tan((beta)/(2))=-(b^(2))/(a^(2))

If alpha and beta are eccentric angles of the ends of a focal chord of the ellipse x^2/a^2 + y^2/b^2 =1 , then tan alpha/2 .tan beta/2 is (A) (1-e)/(1+e) (B) (e+1)/(e-1) (C) (e-1)/(e+1) (D) none of these

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ARIHANT MATHS-ELLIPSE-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the chord, joining two points whose eccentric angles are alpha and ...

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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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