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If the pair of straight lines Ax^(2)+2Hx...

If the pair of straight lines `Ax^(2)+2Hxy+By^(2)=0` be conjugate diameters of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`, then prove that `Aa^(2)=Bb^(2).`

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ARIHANT MATHS ENGLISH-HYPERBOLA-Exercise For Session 3
  1. The diameter of 16x^(2)-9y^(2)=144 which is conjugate to x=2y is

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  2. Tangents drawn from a point on the circle x^2+y^2=9 to the hyperbola x...

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  3. If H=(x^(2))/(a^(2))-(y^(2))/(b^(2))-1=0, C=(x^(2))/(a^(2))-(y^(2))/(b...

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  4. Find the angle between the asymptotes of the hyperbola (x^(2))/(16)-(y...

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  5. If e and e(1), are the eccentricities of the hyperbolas xy=c^(2) and x...

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  6. Find the product of the length of perpendiculars drawn from any point ...

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  7. The number of points on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=3 from w...

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  8. If the sum of the slopes of the normal from a point P to the hyperbola...

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  9. If S=0 is the equation of the hyperbola x^2+4x y+3y^2-4x+2y+1=0 , then...

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  10. A ray emanating from the point (sqrt(41), 0) is incident on the hyperb...

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  11. If a ray of light incident along the line 3x+(5-4sqrt2)y=15 gets refle...

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  12. The equation of the transvers and conjugate axes of a hyperbola are, ...

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  13. Find the equation of that diameter which bisects the chord 7x+y-2=0 of...

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  14. Find the equation of the hyperbola which has 3x-4y+7=0 and 4x+3y+1=0 a...

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  15. The asymptotes of the hyperbola centre of the point (1, 2) are parall...

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  16. If the pair of straight lines Ax^(2)+2Hxy+By^(2)=0 be conjugate diamet...

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  17. A circle cuts the rectangular hyperbola xy=1 in the points (x(r),y(r)...

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