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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 centroid of triangle PQR is `(x-2alpha)^(2)-(y-2beta)^(2)=a^(2)`.

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ARIHANT MATHS-HYPERBOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. A circle with centre (3alpha, 3beta) and of variable radius cuts the ...

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  2. The locus a point P(alpha,beta) moving under the condition that the li...

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  3. Let a hyperbola passes through the focus of the ellipse (x^(2))/(25)+(...

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  4. A hyperbola, having the transverse axis of length 2sin theta, is conf...

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  5. Two braches of a hyperbola

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  6. For the hyperbola (x^2)/(cos^2alpha)-(y^2)/(sin^2alpha)=1 , which of ...

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  7. Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with ve...

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  8. An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The ...

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  9. The circle x^(2)+y^(2)-8x=0 and hyperbola (x^(2))/(9)-(y^(2))/(4)=1 in...

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  10. The circle x^2+y^2-8x=0 and hyperbola x^2/9-y^2/4=1 intersect at the...

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  11. The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1. I...

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  12. Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1If t...

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  13. let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal ...

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  14. Tangents are drawn to the hyperbola x^2/9-y^2/4=1 parallet to the srai...

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  15. Consider the hyperbola H:x^2-y^2=1 and a circle S with centre N(x2,0) ...

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  16. The eccentricity of the hyperbola whose latuscrectum is 8 and conjugat...

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  17. A hyperbola passes through the point P(sqrt(2),sqrt(3)) and has foci a...

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  18. If 2x-y+1=0 is a tangent to the hyperbola (x^2)/(a^2)-(y^2)/(16)=1 the...

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