27. Find the eccentricity, length of latus rectum, foci and the equations of directrices of the ellipse
25x2 +972 - 50x - 36y - 164 = 0.
28
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Answer:
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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