SOLUTION: Locate the center, foci, vertices, ends of latera recta, & draw the ellipse. also compute the eccentricity & find the equation of the directices. 2.x^2/36+y^2/16=1

Question 948467: Locate the center, foci, vertices, ends of latera recta, & draw the ellipse. also compute the eccentricity & find the equation of the directices.
2.x^2/36+y^2/16=1

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!

STANDARD FORM:

CENTER: Center is at (h,k) in this case (0,0). Center is at origin.
FOCI: Focus is (f) from center
Find square root of each side.

Foci are at (,) and (,).
VERTICES: In this case at (+ or - a,0) and a==6
Vertices at (-6,0) and (6,0)

ENDPOINTS OF LATERA RECTA: The latera recta are perpendicular to the major axis at the foci, and have length: . Since half is above and half is below the axis, we need half the length or =16/6=8/3
For the focus at (),), the endpoints of the latus rectum are (,) and (,)
For the focus at (,), the endpoints of the latus rectum are (,) and (,)
ECCENTRICITY: Eccentricity =f/a=
EQUATIONS OF DIRECTRICES: directrix is a line perpendicular to the main axis
on opposite the vertex from the focus, and same distance as the focus from the vertex. The directrix is outside the ellipse. The is a+(a-f) from the center,
or in this case, the directrix to the right of the origin is x== and to the left of the origin x=-().

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