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A circle with centre `(3alpha, 3beta)` and of variable radius cuts the rectangular hyperbola `x^(2)-y^(2)=9a^(2)` at the points `P, Q, S, R`. Prove that the locus of the triangle PQR is `(x-2alpha)^(2)-(y-2beta)^(2)=a^(2)`.

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A DAS GUPTA-Ellipse and Hyberbola-EXERCISE
  1. A normal to the hyperbola x^2-4y^2=4 meets the x and y axes at A and B...

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

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

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

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

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

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

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  8. The eccentricity of a rectangular hyperbola, is

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

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

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

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

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

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

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

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

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

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

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

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

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