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If the hyperbola x^(2)-y^(2)=4 is rotate...

If the hyperbola `x^(2)-y^(2)=4` is rotated by `45^(@)` in the anticlockwise direction about its center keeping the axis intact, then the equation of the hyperbola is `xy=a^(2)`, where `a^(2)` is equal to _____________.

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
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  2. If L is the length of the latus rectum of the hyperbola for which x = ...

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  3. If the chord x cos theta alpha+y sin alpha=p of the hyperbola (x^(2))...

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  4. If the vertex of a hyperbola bisects the distance between its center ...

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  5. If the distance between two parallel tangents drawn to the hyperbola (...

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  6. The area of triangle formed by the tangents from the point (3, 2) to t...

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  7. If a variable line has its intercepts on the coordinate axes e and e^(...

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  8. If tangents drawn from the point (a, 2) to the hyperbola (x^(2))/(16)-...

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  9. If the hyperbola x^(2)-y^(2)=4 is rotated by 45^(@) in the anticlockwi...

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  10. The coordinates of a point on the hyperbola (x^2)/(24)-(y^2)/(18)=1 wh...

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  11. If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^...

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  12. The sides AC and AB of a DeltaABC touch the conjugate hyperbola of the...

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  13. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 pa...

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  14. If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , t...

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  15. The locus of a point whose chord of contact with respect to the circle...

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  16. The locus of the feet of the perpendiculars drawn from either focus on...

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  17. If the line 2x+sqrt6y=2 touches the hyperbola x^2-2y^2=4, then the po...

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  18. Consider the graphs of y=Ax^(2) and y^(2)+3=x^(2)+4y, where A is a pos...

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  19. The eccentricity of the hyperbola |sqrt((x-3)^(2)+(y-2)^(2))-sqrt((x...

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  20. If y = mx+c is tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)...

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