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If e(1) and e(2) are eccentricities of t...

If `e_(1)` and `e_(2)` are eccentricities of the ellipse `(x^(2))/(18)+(y^(2))/(4)=1` and the hyperbola `(x^(2))/(9)-(y^(2))/(4)=1` respectively, then the relation between `e_(1)` and `e_(2)` is

A

` 3 e_(1)^(2)+e_(2)^(2)=2`

B

`e_(1)^(2)+2 e_(2)^(2)=3`

C

`2 e_(1)^(2)+e_(2)^(2)=3`

D

`e_(1)^(2)+3 e_(2)^(2)=2`

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-ELLIPSE-QUESTION BANK
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  2. If the tangents drawn from a point (1,2 sqrt(3)) to the ellipse (x^(2)...

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  3. If e(1) and e(2) are eccentricities of the ellipse (x^(2))/(18)+(y^(2)...

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  4. The tangents at the ends of the latus rectum L S(1) L^(prime) of the e...

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  5. The tangent to the ellipse (x^(2))/(25)+(y^(2))/(16)=1 at the end of t...

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  6. Area of the quadrilateral formed by the tangents at the ends of latus ...

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  7. The eceentricity of the ellipse whose axes are the coordinate axes and...

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  8. Area of the greatest rectangle that can be inseribed in the ellipse (x...

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  9. Find the equation of the ellipse whose centre is at the origin and maj...

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  10. The equation of the ellipse whose focus is (1,-1) the directrix the li...

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  11. The length of the latus rectum of the ellipse 3 x^(2)+4y^(2)=12 is

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  12. If e is the eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)...

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  13. The eccentricity of the ellipse 9x^(2) + 25y^(2) = 225 is

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  14. The length of the latus rectum of the ellipse 49 x^(2)+64 y^(2)=3136

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  15. The P is any point on the ellipse 4 x^(2)+16 y^(2)=64 whose foci are S...

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

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  17. Length of the latus rectum of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 ...

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  18. The equation of the ellipse whose one focus is at (4,0) and whose ecce...

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  19. The centre of the ellipse 9 x^(2)+5 y^(2)-36 x-50 y+116=0 is

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  20. If y=x+c is a tangent to the ellipse 9 x^(2)+16 y^(2)=144, thenc=

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