SOLUTION: Write the equation of the ELLIPSE that satisfies the given conditions Vertices (-5,0) and (5,0) length of latus rectum 8/5

Algebra ->  Finance -> SOLUTION: Write the equation of the ELLIPSE that satisfies the given conditions Vertices (-5,0) and (5,0) length of latus rectum 8/5       Log On


   

Question 1190960: Write the equation of the ELLIPSE that satisfies the given conditions
Vertices (-5,0) and (5,0) length of latus rectum 8/5

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation of the ELLIPSE that satisfies the given conditions
given:
Vertices (-5,0) and (5,0) ->shows common y coordinate 0.
So x+axis is major axis and y axis is minor axis, therefore+a greater than b

Standard equation for this ellipse is:

%28x+-+h%29%5E2%2Fa%5E2+%2B+%28y+-+k%29%5E2+%2Fb%5E2=+1

the center is half way between vertices: C+(%28-5%2B5%29%2F2,%280%2B0%29%2F2)=(0.0)=>h=0 and k=0
2a+ is the distance between vertices and center=>2a=10->a=5
length of latus rectum 8%2F5-> In this ellipse latus rectum is 8%2F5 means 2b%5E2%2Fa=8%2F5
so, 2b%5E2=8 ->b%5E2=4+
and a=5 units

your equation is:

%28x+-+0%29%5E2%2F5%5E2+%2B+%28y+-+0%29%5E2+%2F4=+1

x%5E2%2F25+%2B+y%5E2+%2F4=+1