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The length of the intercepts on the x an...

The length of the intercepts on the x and y-axes of a circle are 2a and 2b unit respectively. Prove that the locus of the centre of the circle is hyperbola whose equation `x^2-y^2=a^2-b^2`. Translating the origin to a suitable point show that the equation `5x^2-4y^2-20x-8y-4=0` represents a hyperbola. Find its eccentricity, coordinates of foci and equations of the directrices.

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PATHFINDER-PARABOLA, ELLIPSE AND HYPERBOLA-QUESTION BANK
  1. The centre of the hyperbola 9x^2-16y^2-18x+64y-199=0 is

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. In a rectangular hyperbola x^2-y^2=a^2, prove that SP.S'P=CP^2, wher...

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  17. If e1 and e2 be the eccentricities of a hyperbola and its conjugate, s...

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

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  19. The length of the intercepts on the x and y-axes of a circle are 2a an...

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  20. If the chord joining the points (asectheta, btantheta)and (asecphi, bt...

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