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Show that the equation x^2-2y^2-2x+8y-1=...

Show that the equation `x^2-2y^2-2x+8y-1=0` represents a hyperbola. Find the coordinates of the centre, lengths of the axes, eccentricity, latusrectum, coordinates of foci and vertices, equations of the directrices of the hyperbola.

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A DAS GUPTA-Ellipse and Hyberbola-EXERCISE
  1. Find the equation of an ellipse hose axes lie along the coordinate ...

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  2. if in a hyperbola the eccentricity is sqrt3 and the distance between t...

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  3. Show that the equation x^2-2y^2-2x+8y-1=0 represents a hyperbola. Find...

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  4. Find the equations of normal to the parabola y^2=4a x at the ends of t...

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  5. Let P be a variable point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 wit...

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  6. The number of maximum normals that can be drawn from any point to an e...

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  7. If a tangent to the ellipse x^2/a^2+y^2/b^2=1, whose centre is C, me...

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  8. Find the length of the chord of the ellipse x^2/25+y^2/16=1, whose mid...

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  9. If the line lx+my+n=0 touches the hyperbola (x^(2))/(a^(2))-(y^(2))/(b...

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  10. Show that 3x^(2) - 3y^(2) - 18x + 12y + 2 = 0 represents a rectangular...

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  11. The point P on the ellipse 4x^2+9y^2=36 is such that the are of the P...

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  12. If the tangent and normal to a rectangular hyperbola cut off intercept...

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  13. The equation 14x^2 - 4xy+ 11y^2 - 44x - 58y + 71 = 0 represents

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  14. If e is eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(...

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  15. Find the eccentric angle of a point on the ellipse x^2 + 3y^2 = 6 at a...

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  16. Which of the following is an exterior point of the ellipse 16x^2+9y^2-...

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  17. The line 3x+5y=k touches the ellipse 16x^(2)+25y^(2)=400 ,if k is

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  18. Find the equaiton of the tangents to the hyperbola x^2 - 2y^2 = 18 whi...

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  19. A point on the ellipse x^2+3y^2=37 where the normal is parallel to the...

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  20. if the ordinate of the point of contact be 2 then the equation of the ...

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