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P and Q be the extremities of the two co...

P and Q be the extremities of the two conjugate diameters of the ellipse `x^2/a^2+y^2/b^2=1`, Show that the locus of the middle point of PQ is `x^2/a^2+y^2/b^2=1/2`.

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PATHFINDER-PARABOLA, ELLIPSE AND HYPERBOLA-QUESTION BANK
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  2. If the chord joining the points P(theta)' and 'Q(phi)' of the ellipse ...

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  5. If the latus rectum of a hyperbola is equal to half of its transverse ...

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  6. The centre of the hyperbola 9x^2-16y^2-18x+64y-199=0 is

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  7. If foci of the ellipse (x^(2))/(16) + (y^(2))/(b^(2)) = 1 coincide wit...

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  8. The eccentricity of the hyperbola x^2-y^2=4 is

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  9. Find the equation to the locus represented by the parametric equation...

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  10. The equation of the auxiliary circle of the hyperbola x^2/a^2-y^2/b^2=...

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  11. The eccentricity of the curve 9x^2-25y^2=225 is

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  12. The foci of the hyperbola 4x^2-9y^2=36 is

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  13. If the length of conjugate axis and the length of latus rectum of a hy...

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  14. The equations of directrices of hyperbola 4x^2-9y^2-16x-54y-101=0 are

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

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  16. Show that the difference of the distances from each focus of any point...

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  17. Show that the eccentricities of the hyperbolas x^2/16-y^2/9=1 and x^2/...

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  18. Find the equation of the hyperbola, whose axes are axes of coordinates...

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  19. Find the equation of the hyperbola whose vertices are (+-4,0) and foci...

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  20. Show that 3x^2-3y^2-18x+12y+2=0 represents a rectangular hyperbola. Fi...

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