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Standard XII

Mathematics

Definition of Hyperbola

If e and ...

Question

If $e$ and $e^{'}$ be the eccentricities of two conics $S$ $=$ $0$ and $S^{'}$ $=$ $0$ and if $e^{2} + e^{' 2} = 3$ , then both $S$ and $S^{'}$ can be

hyperbolas

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ellipses

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parabolas

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none of these

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Solution

The correct option is A hyperbolas
For a parabola the eccentricity is 1.
$∴ e^{2} + {e^{'}}^{2} = 1 + 1 = 2$
For an ellipse the eccentricity is less than 1
$∴$ For a hyperbola the eccentricity is greater than 1. So, the conics can be hyperbolas
Hence, option 'A' is correct.

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Similar questions

Q. If

e

and

e^{'}

be the eccentricities of two conics

S = 0

and

S^{'} = 0

and if

e^{2} + {e^{'}}^{2} > 2

, then

S

and

S^{'}

can be

Q. If

e

and

e^{'}

be the eccentricities of two conics

S

and

S^{'}

such that

e^{2} + (e^{'})^{2} = 3,

then both

S

and

S^{'}

are

$e_{1}$ 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

Q. Change

Q_{1}

and

Q_{2}

lie inside and outside respectively of a closed surface

S

. Let

E

be the field at any point on

S

ϕ

be the flux of

E

(electric field) over

S

	List-I		List-II
(P)	If $Q_{1} = 0$ and $Q_{2} \neq 0$ then	(1)	Both $E$ and $ϕ$ will change
(Q)	If $Q_{1} \neq 0$ and $Q_{2} = 0$ then	(2)	$E \neq 0$ and $ϕ \neq 0$
(R)	If $Q_{2}$ changes	(3)	net electric field will change but $ϕ$ will not change
(S)	If $Q_{1}$ changes	(4)	$E \neq 0$ but $ϕ = 0$

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If e and e′ be the eccentricities of two conics S = 0 and S′ = 0 and if e2+e′2=3, then both S and S′ can be

The correct option is A hyperbolasFor a parabola the eccentricity is 1. ∴e2+e′2=1+1=2For an ellipse the eccentricity is less than 1∴ For a hyperbola the eccentricity is greater than 1. So, the conics can be hyperbolasHence, option 'A' is correct.

If $e$ and $e^{'}$ be the eccentricities of two conics $S$ $=$ $0$ and $S^{'}$ $=$ $0$ and if $e^{2} + e^{' 2} = 3$ , then both $S$ and $S^{'}$ can be

The correct option is A hyperbolas
For a parabola the eccentricity is 1.
$∴ e^{2} + {e^{'}}^{2} = 1 + 1 = 2$
For an ellipse the eccentricity is less than 1
$∴$ For a hyperbola the eccentricity is greater than 1. So, the conics can be hyperbolas
Hence, option 'A' is correct.