NelaO327883 NelaO327883
  • 27-10-2022
  • Mathematics
contestada

Find the distance between the foci of an ellipse. The lengths of the major and minor axes are listen respectively. 50 and 14

Respuesta :

AnabD659392 AnabD659392
  • 27-10-2022

ANSWER :

48

EXPLANATION :

The length of the major axis (2a) is 50 and the length of the minor axis (2b) is 14

So :

[tex]\begin{gathered} 2a=50 \\ a=25 \\ \\ 2b=14 \\ b=7 \end{gathered}[/tex]

The distance between the foci is 2c, and the formula of c is :

[tex]c^2=a^2-b^2[/tex]

Using the formula above :

[tex]\begin{gathered} c^2=25^2-7^2 \\ c^2=576 \\ c=\sqrt{576} \\ c=24 \end{gathered}[/tex]

Then the distance of the foci is 2c = 2(24) = 48

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