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Prove that the locus of the middle-point...

Prove that the locus of the middle-points of the chords of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`which pass through a fixed point `(alpha, beta)` is a hyperbola whose centre is `((alpha)/(2), (beta)/(2))`.

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A DAS GUPTA-Ellipse and Hyberbola-EXERCISE
  1. Find the locus of the foot of the perpendicular drawn from the cent...

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  2. A variable straight line of slope 4 intersects the hyperbola xy=1 at t...

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  3. Prove that the locus of the middle-points of the chords of the hyperbo...

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  4. A normal to the hyperbola x^2-4y^2=4 meets the x and y axes at A and B...

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  5. A circle cuts two perpendicular lines so that each intercept is of giv...

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  6. A circle with centre (3alpha, 3beta) and of variable radius cuts the ...

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  7. The locus of the point of intersection of the tangents at the end-poin...

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  8. Find the locus of the-mid points of the chords of the circle x^2 + y^2...

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  9. If alpha and beta be the angles subtended by the major axis to an elli...

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  10. The equation x^2-3xy+y^2+10x-10y+21=0represents a having its centre at...

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  11. The eccentricity of a rectangular hyperbola, is

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  12. Equation of the ellipse whose focus is (6,7) directrix is x + y + 2 = ...

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  13. The latus rectum of an ellipse is 10 and the minor axis Is equal to th...

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  14. Find the equation of an ellipse hose axes lie along the coordinate ...

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

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

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

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

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

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

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