SOLUTION: Write the equation of the ellipse in standard form that satisfies the given conditions. Draw the ellipse, its focus, and directrix. 2.) The vertices are at (3,-3) and (3,5) and

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equation of the ellipse in standard form that satisfies the given conditions. Draw the ellipse, its focus, and directrix. 2.) The vertices are at (3,-3) and (3,5) and      Log On


   

Question 1045393: Write the equation of the ellipse in standard form that satisfies the given conditions. Draw the ellipse, its focus, and directrix.
2.) The vertices are at (3,-3) and (3,5) and the length of the minor axis is 6.
Please help me with my homework :'( Thank you so much. It would really sooooo much to me and would be greatly appreciated ^_^
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Standard Form of an Equation of an Ellipse is %28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1+
where Pt(h,k) is the center. (a variable positioned to correspond with major axis)
a and b are the respective vertices distances from center.
The foci distances from center: c = ±sqrt%28a%5E2-b%5E2%29 where a > b
eccentricity = c/a
vertices are at (3,-3) and (3,5) |major axis 8, Center: (3,1) a = 4
minor axis is 6 | b = 3
%28x-3%29%5E2%2F4%5E2+%2B+%28y-1%29%5E2%2F3%5E2+=+1+
c = ±sqrt%28a%5E2-b%5E2%29 , c = ±sqrt%2816-9%29 c = ± sqrt%287%29
foci: (3, 1- sqrt%287%29) and (3, 1+ sqrt%287%29)
The directrices are a distance aČ/c in both directions from the center of the ellipse.
directrix: y = 1 + 16/sqrt%287%29) and y = -3 - sqrt(7