Answers

2015-09-16T04:52:07+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
X² / a²  + y² / b²  = 1 

where a = semi major axis,    b = semi minor axis.
center of ellipse is  (0,0)  and the ellipse is symmetric about X and Y axes.

Latus Rectum = 2 b² / a = 5
     eccentricity :    e = 2/3
     so     b² = a² (1 - e²) = a² * 5/9

      hence,  a = 2 b² / 5  = 2 a²/9        =>  a = 9/2
           b = 3√5 / 2

so equation is :  4 x²/9 +  4 y² /45 = 1
=========================
2)
   distance between focii =  2 a e = 2 * b      given
                       so b = a e

      we know that          b² =  a² - a² e²  =  a² - b²
                             =>  b = a/√2
                                   e = 1/√2
 
             2 b² / a = latus rectum = 10
             so  2 * a / 2   =  10
               =>  a = 5        and  b  = 5/√2
 
         so  x²/25 + 2 y² /25  = 1

1 5 1
click on thanks button above pls
select best answer pls