3.
Find the equation of the ellipse referred to its major
and minor axes as the coordinate axes X, Y-respec-
tively with latus rectum of length 4, and distance be-
tween foci 412.
Answers
Answered by
1
Step-by-step explanation:
We have 9x
2
+16y
2
−36x+32y−92=0
⇒9(x
2
−4x)+16(y
2
+2y)=92
⇒9(x
2
−4x+4)+16(y
2
+2y+1)=92+36+16=144
⇒9(x−2)
2
+16(y+1)
2
=144
⇒
16
(x−2)
2
+
9
(y+1)
2
=1
⇒a
2
=16,b
2
=9
Thus eccentricity, e=
1−
a
2
b
2
=
1−
16
9
=
4
7
and length of latus rectum =
a
2b
2
=
2
9
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