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If \mathrm{e \text { and } e^{\prime}}  be the eccentricities of two conics \mathrm{ S}=0 and \mathrm{ S^{\prime}}=0 and

if \mathrm{e^2+e^{\prime 2}=3 }  then both \mathrm{S \text { and } S^{\prime}}, can be

Option: 1

hyperbolas


Option: 2

ellipses


Option: 3

parabolas


Option: 4

none of these


Answers (1)

best_answer

For a parabola the eccentricity is 1.

\mathrm{\therefore \quad e^2+e^{\prime 2}=1+1=2}

For an ellipse the eccentricity is less then 1.

\mathrm{\therefore \quad 0<e<1,0<e^{\prime}<1 \Rightarrow e^2+e^{\prime 2}<2}.

For a hyperbola the eccentricity is greater than 1.

So, the conics can be hyperbolas.

Posted by

Deependra Verma

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