The difference of the focal semi axes of an ellipse and a hyperbola is equal to $4$.If the ratio of their eccentricities is $\frac{3}{7}$.

An ellipse and a hyperbola have their principal axes along the coordinate axes and have a common foci separated by a distance $2\sqrt{13}$,the difference of their focal semi axes is equal to $4$.If the ratio of their eccentricities is $\frac{3}{7}$.Find the equation of these curves.

The distance between the foci of both ellipse and hyperbola is $2\sqrt{13}$.

So $2c_1=$distance between the foci of ellipse$=2\sqrt{13}$

$2c_2=$distance between the foci of hyperbola$=2\sqrt{13}$

$\frac{\text{eccentricity of ellipse}}{\text{eccentricity of hyperbola}}=\frac{3}{7}$

I do not understand what is the meaning of "the difference of their focal semi axes" and how to proceed further.

• – lab bhattacharjee Jan 9 '16 at 15:03
• @labbhattacharjee,i did not understand after reading this link.See if $c_1=c_2$,then how is $c_1-c_2=4$ possible? – user1557 Jan 9 '16 at 15:53