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let the eccentricity of the hyperbola x^...

let the eccentricity of the hyperbola `x^2/a^2-y^2/b^2=1` be reciprocal to that of the ellipse `x^2+4y^2=4.` if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is `x^2/3-y^2/2=1` (b) a focus of the hyperbola is `(2,0)` (c) the eccentricity of the hyperbola is `sqrt(5/3)` (d) the equation of the hyperbola is `x^2-3y^2=3`

A

the equation of the hyperbola is `(x^(2))/(3)-(y^(2))/(2)=1`

B

a focus of the hypberbola is `sqrt((3),0)`

C

the eccentricity of the hyperbola is `sqrt(5//3)`

D

the equation of the hyperbola is `x^(2)-3y^(2)=3`

Text Solution

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The correct Answer is:
D
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MCGROW HILL PUBLICATION-HYPERBOLA-SOLVED EXAMPLES LEVEL 1(SINGLE CORRECT ANSWER TYPE QUESTIONS)
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  2. If the circle x^2+y^2=a^2 intersects the hyperbola xy=c^2 in four poin...

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  3. Show that the normal to the rectangular hyperbola xy = c^(2) at the po...

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  4. If the normal at P to the rectangular hyperbola x^(2) - y^(2) = 4 meet...

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  5. If e(1),e(2) are the eccentricites of the hyperbla 2x^(2)-2y^(2)=1 an...

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  7. The equation of the hyperbola whose foci are (-2, 0) and (2,0) and ecc...

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

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  9. If the normal at the point P intersects the x-axis at (9, 0) then the ...

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  10. The foci of the ellips (x^(2))/( 16) +(y^(2))/( b^(2) ) =1 and the h...

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  11. If the tangents at the point (a sec alpha, b tan alpha) to the hyperbo...

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  12. The distannce between the tangent to the hyperbola (x^(2))/(4)-(y^(2))...

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  13. Find the locus of the middle points of the normals chords of the recta...

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  14. If y = mx + 6 is a tangent to the hyperbola he parabola y^(2) = 4ax, t...

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  15. P is a point on the hyperbola The tangent at P meets the transverse a...

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  16. The product of the perpendiculars from the foci on any tangent to the ...

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  17. If the normal at P on the hyperbola meets the transverse axis at G, S ...

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  18. If the chords of contacts of the tangents from the points (x y,) and (...

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

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  20. Normal at point (5, 3) to the rectangular hyperbola x y - y - 2 x - 2 ...

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