E 1 and e 2 are the eccentricities of two conics S and S 1- If e 12- e 22-3 then both S and S 1 can beA- ellipseB- parabolasC- hyperbolasD- circles

The correct option is C hyperbolas Given e_1^2 + e_2^2 = 3 ∴ e_1 and e_2 gt; 1 ) ∴ Both are hyperbolas . ...

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Standard XII

Mathematics

Eccentricity of Hyperbola

e 1 and e 2 a...

Question

$e_{1}$ and $e_{2}$ are the eccentricities of two conics S and $S^{1}$ . If ${e_{1}}^{2} + {e_{2}}^{2}$ = 3 then both S and $S^{1}$ can be

ellipse

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parabolas

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hyperbolas

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circles

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Solution

The correct option is C
hyperbolas

Given $e_{1}^{2} + e_{2}^{2} = 3$ $∴$ $e_{1} a n d e_{2} > 1)$

$∴$ Both are hyperbolas .

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Similar questions

$e_{1}$ and $e_{2}$ are the eccentricities of two conics S and $S^{1}$ . If ${e_{1}}^{2} + {e_{2}}^{2}$ = 3 then both S and $S^{1}$ can be

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e_{1}

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$I f e_{1} i s t h e e c c e n t r i c i t y o f t h e c o n i c 9 x^{2} + 4 y^{2} = 36 a n d e^{2} i s t h e e c c e n t r i c i t y o f t h e c o n i c 9 x^{2} - 4 y^{2} = 36, t h e n$

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P, Q

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P Q = P R = \frac{2 \sqrt{2}}{3} .

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Q. Let

E_{1}

and

E_{2}

be the two ellipses centred at origin. The major axis of

E_{1}

and

E_{2}

lie along the

x -

axis and

y -

axis respectively. Let

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be the circle

x^{2} + (y - 1)^{2} = 2,

the straight line

x + y = 3

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and

E_{2}

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and

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respectively such that

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e_{2}

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e1 and e2 are the eccentricities of two conics S and S1. If e12+e22 = 3 then both S and S1 can be

The correct option is C hyperbolas Given e21+e22=3 ∴ e1ande2>1) ∴ Both are hyperbolas .

$e_{1}$ and $e_{2}$ are the eccentricities of two conics S and $S^{1}$ . If ${e_{1}}^{2} + {e_{2}}^{2}$ = 3 then both S and $S^{1}$ can be

The correct option is C
hyperbolas

Given $e_{1}^{2} + e_{2}^{2} = 3$ $∴$ $e_{1} a n d e_{2} > 1)$

$∴$ Both are hyperbolas .