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Test Index
TS EAMCET 19-July-2022 Shift 2 Solved Paper
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© examsnet.com
Question : 58
Total: 160
Statement I : The equation of the directrix of the ellipse
4
x
2
+
y
2
−
8
x
−
4
y
+
4
=
0
is
3
y
=
6
−
4
√
3
Statement II : The equation of the latus rectum of the ellipse
x
2
+
4
y
2
−
4
x
−
8
y
+
4
=
0
is
y
=
2
+
√
3
Which of the above statement(s) is(are) true?
Statement I is true, but Statement II is false
Statement II is true, but Statement I is false
Both Statement I and Statement II are true
Both Statement I and Statement II are false
Validate
Solution:
Statement I : Given, equation of ellipse is
4
x
2
+
y
2
−
8
x
−
4
y
+
4
=
0
4
x
2
−
8
x
+
4
+
y
2
−
4
y
+
4
=
4
⇒
4
(
x
−
1
)
2
+
(
y
−
2
)
2
=
4
⇒
(
x
−
1
)
2
1
+
(
y
−
2
)
2
4
=
1
The origin of the vertex is
(
1
,
2
)
.
Here,
a
2
=
4
,
b
2
=
1
e
=
√
1
−
b
2
a
2
=
√
1
−
1
4
=
√
3
2
Equation of directrix is
y
−
k
=
±
a
e
⇒
y
−
2
=
±
2
√
3
∕
2
⇒
y
−
2
=
±
4
√
3
3
⇒
3
y
−
6
=
±
4
√
3
⇒
3
y
=
6
±
4
√
3
∴
Statement I is true.
Statement II : Given, equation of ellipse
x
2
+
4
y
2
−
4
x
−
8
y
+
4
=
0
⇒
x
2
−
4
x
+
4
+
4
y
2
−
8
y
+
4
=
4
⇒
(
x
−
2
)
2
+
4
(
y
−
1
)
2
=
4
⇒
(
x
−
2
)
2
4
+
(
y
−
1
)
2
1
=
1
∴
X
2
4
+
Y
2
1
=
1
, where
X
=
x
−
2
and
Y
=
y
−
1
e
=
√
1
−
1
4
=
√
3
2
Coordinate of focus
=
(
±
a
e
,
0
)
=
(
±
√
3
,
0
)
Equation of latusrectum
X
=
±
√
3
⇒
x
−
2
=
±
√
3
⇒
x
=
2
±
√
3
∴
Statement II is false.
© examsnet.com
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