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If e(1) be the eccentricity of a hyperbo...

If `e_(1)` be the eccentricity of a hyperbola and `e_(2)` be the eccentricity of its conjugate, then show that the point `(1/e_(1) , 1/e_(2))` lies on the circle `x^(2) + y^(2) = 1`.

A

`x^(2) + y^(2) = 0`

B

`x^(2) + y^(2) = 1`

C

`x^(2) + y^(2) = 2`

D

`x^(2) + y^(2) = 3`

Text Solution

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The correct Answer is:
B
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MARVEL PUBLICATION-CIRCLE AND CONICS -MULTIPLE CHOICE QUESTIONS
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  2. If e(1) , e(2) " and " e(3) the eccentricities of a parabola , and e...

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  3. If e(1) be the eccentricity of a hyperbola and e(2) be the eccentricit...

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  4. If t is a non-zero parameter , then the locus of the point of intersec...

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  5. The locus represented by x=a/2(t+1/t), y=a/2(t-1/t) is

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  6. A hyperbola, centred at the prigin, has transverse axis 2a. If it pass...

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  7. For the hyperbola (x^(2))/(cos^(2) alpha ) - (y^(2))/(sin^(2) alpha )...

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  8. Point P, Q and R on the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) =...

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  9. The equation of the conic with focus at (1,-1), directrix along x -y +...

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  10. The equation x = (e ^(t) + e ^(-t))/(2), y = (e ^(t) -e^(-t))/(2), t i...

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  11. Locus of the point of intersection of the lines mx sqrt(3) + my - ...

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  12. Write the equation of the hyperbola whose vertices are (+-3,0) and foc...

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  13. lf the eccentricity of the hyperbola x^2-y^2(sec)alpha=5 is sqrt3 ti...

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  14. Standard equation of the hyperbola having distance between foci to 32 ...

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  15. If 0 lt alpha lt (pi)/(2) and the eccentricity of the ellipse x^...

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  16. If P is a point on the hyperbola 16x^(2) - 9y^(2) = 144 whose foci ar...

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  17. If the latus rectum of an hyperbola be 8 and eccentricity be (3)/( sqr...

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  18. Eccentricity of the hyperbola passing through (3,0) and (3 sqrt(2),2) ...

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  19. Find the equation of the hyperbola whose conjugate axis is 5 and th...

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  20. The length of the transverse axis of a hyperbola is 7 and it passes th...

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