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If the hyperbola xy=c^(2) intersects the...

If the hyperbola `xy=c^(2)` intersects the circle `x^(2)+y^(2)=a^(2)" is four points "P(x_(1),y_(1)), Q(x_(2),y_(2)), R(x_(3),y_(3)) and S(x_(4),y_(4))` then show that
(i) `x_(1)+x_(2)+x_(3)+x_(4)=0`
(ii) `y_(1)+y_(2)+y_(3)+y_(4)=0`
(iii) `x_(1)x_(2)x_(3)x_(4)=c^(4)`
(iv) `y_(1)y_(2)y_(3)y_(4)=c^(4)`

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AAKASH SERIES-HYPERBOLA-Additional Exercise
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  2. A normal to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 cuts the axes...

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  3. Let P (a sec theta, b tan theta) and Q (a sec phi, b tan theta) where ...

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  4. Prove that the locus of the point of intersection of tangents at the e...

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  5. Prove that the portion of the tangent of the rectangular hyperbola int...

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  6. If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is ...

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  7. Let P (a sec theta, b tan theta) and Q (a sec phi, b tan theta) where ...

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  8. If x=9 is the chord of contact of tangents of x^(2)-y^(2)=9, then show...

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  9. Show that the equationi of the rectanglar hyperbola whose focus is (1,...

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  10. The hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 has its conjugate axis 5 and p...

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  11. Tangents are drawn from points on the hyperbola x^(2)/9-y^(2)/4=1 to t...

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  12. If a hyperbola passes through a focus of the ellipse and it transverse...

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  13. A hyperbola having the transverse axis of length 2 sin theta, is confo...

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  14. An ellipse has eccentricity 1/2 and the focus at the point P(1/2,1). I...

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  15. The locus represented by x=(a)/(2)(t+(1)/(t)),y=(a)/(2)(t-(1)/(t)) i...

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  16. If the normal at (x(i) y(i)) i=1,2,3,4 on xy=c^2 meet at the point (al...

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  17. Given the base BC of the triangle ABC and if angleC-angleB=k, a consta...

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  18. The ordinate of any point P on the hyperbola 25x^(2)-16y^(2)=400 is pr...

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  19. Given the base of the triangle and the sum of tangent of base angles a...

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  20. From a fixed point A(x(1),y(1)) a variable straight line is drawn to c...

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