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Question
Mathematics
The equation of a directrix of the ellipse (x2/16) + (y2/25) = 1 is
Q. The equation of a directrix of the ellipse
16
x
2
+
25
y
2
=
1
is
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VITEEE
VITEEE 2007
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A
3y = 5
B
y = 5
C
3y = 25
D
y = 3
Solution:
Equation of ellipse
b
2
x
2
+
a
2
y
2
=
1
, where a > b
Given,
16
x
2
+
75
y
2
=
1
⇒
b
=
4
,
a
=
5
But
e
=
1
−
a
2
b
2
=
1
−
25
16
⇒
e
=
5
3
∴
equation of directrix
y
=
±
e
a
∴
y
=
±
5
3
5
⇒
3
y
=
±
25