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TS EAMCET 20-July-2022 Shift 2 Solved Paper
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© examsnet.com
Question : 58
Total: 160
If
m
is the length of the latus rectum and
n
is the length of the major axis of the ellipse
25
x
2
+
16
y
2
−
150
x
−
64
y
−
111
=
0
, then the ordered pair
(
m
,
n
)
=
(
16
5
,
10
)
(
32
5
,
10
)
(
25
2
,
8
)
(
25
4
,
8
)
Validate
Solution:
Given, equation of ellipse
25
x
2
+
16
y
2
−
150
x
−
64
y
−
111
=
0
⇒
25
x
2
−
150
x
+
225
+
16
y
2
−
64
y
+
64
=
111
+
225
+
64
⇒
(
5
x
−
15
)
2
+
(
4
y
−
8
)
2
=
400
⇒
25
(
x
−
3
)
2
+
16
(
y
−
2
)
2
=
400
⇒
(
x
−
3
)
2
400
25
+
(
y
−
2
)
2
400
16
=
1
⇒
(
x
−
3
)
2
16
+
(
y
−
2
2.
25
=
1
Let
x
−
3
=
X
and
y
−
2
=
Y
∴
X
2
16
+
Y
2
25
On comparing with
X
2
b
2
+
Y
2
a
2
=
1
∴
a
2
=
25
and
b
2
=
16
Length of latusrectum
(
m
)
=
2
b
2
a
=
2
×
16
5
=
32
5
and length of the major axis
(
h
)
=
2
a
=
2
×
5
=
10
∴
(
m
,
n
)
=
(
32
5
,
10
)
© examsnet.com
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