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The line `2x + y = 1` is tangent to the hyperbola `x^2/a^2-y^2/b^2=1`. If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is

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MOTION-HYPERBOLA-EXERCISE-4 (Level-II)
  1. If a hyperbola passes through the focus of the ellipse x^(2)/25+y^(2)/...

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  2. Let ABCD be a square of side length 2 units. C2 is the circle through ...

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  3. Let ABCD be a square of side length 2 units. C(2) is the fircle throug...

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  4. Let ABCD be a square of side length 2 units. C(2) is the circle throug...

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

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  6. Match the statements in Column I with the properties in Column II. A

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  7. Let 'a' and 'b' be non-zero real numbers. Then, the equation (ax^2+ by...

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

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  9. Match the conics in column I with statements/ex- pressions in Column I...

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

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

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

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

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  14. Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=...

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

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  17. Let H :(x^2)/(a^2)-(y^2)/(b^2)=1 , where a > b >0 , be a hyperbola in ...

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