Question

If $e$ and $e^{\prime }$ be the eccentricities of two conics $S$ and $S^{\prime }$ such that $e^2+(e^{\prime }{)}^2=3,$ then both $S$ and $S^{\prime }$ are

• A. Ellipses
• B. Parabolas
• C. Hyperbolas
• D. None of these

Answer 1

The correct option is C Hyperbolas

For a parabola the eccentricity is $1$

$\therefore e^2+e^{\prime 2}=1+1=2$

For an ellipse the eccerntricity is less than $1$

$\therefore$ for a hyperbola the eccentricity is greater than $1$

So, the conics can be hyperbolas

Hence, hyperbola correct.