SOLUTION: Find the standard form of the equation of each ellipse satisfying the given conditions. Endpoints of major axis: (2,2) and (8,2) Endpoints of minor axis: (5,3) and (

Algebra ->  Pythagorean-theorem -> SOLUTION: Find the standard form of the equation of each ellipse satisfying the given conditions. Endpoints of major axis: (2,2) and (8,2) Endpoints of minor axis: (5,3) and (      Log On


   

Question 481493: Find the standard form of the equation of each ellipse satisfying the given conditions. Endpoints of major axis: (2,2) and (8,2)
Endpoints of minor axis: (5,3) and (5,1)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
find the length using distance formula
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%288-2%29%5E2+%2B+%282-2%29%5E2%29=+6+


For more on this concept, refer to Distance formula.


so, major axis is 6 long
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%285-5%29%5E2+%2B+%281-3%29%5E2%29=+2+


For more on this concept, refer to Distance formula.


minor axis is 2 long
The length of the horizontal axis is 2a.
2a=6
a=3
The length of the vertical axis is 2b.
2b=2
b=1
x%5E2%2F3%5E2+%2By%5E2%2F1%5E2+=1
x%5E2%2F9+%2By%5E2+=1