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Manipal Entrance Test 2015 Math Paper
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© examsnet.com
Question : 51
Total: 70
The two tangents to the curve
a
x
2
+
2
h
x
y
+
b
y
2
=
1
,
a
>
0
at the points where it crosses
X
-axis, are
parallel
perpendicular
None of these
inclined at an angle
π
4
Validate
Solution:
At the point where the given curve crosses X-axis,
we have
y
=
0
⇒
a
x
2
=
1
[putting
y
=
0
in
a
x
2
+
2
h
y
x
+
b
y
2
=
1
]
⇒
x
=
±
1
√
a
Thus, the given curve cuts
X
-axis at
P
1
√
a
,
0
)
and
Q
(
−
1
√
a
,
0
)
Now,
a
x
2
+
2
h
x
y
+
b
y
2
=
1
On differentiating both sides w.r.t. x, we get
2
a
x
+
2
h
(
x
d
y
d
x
+
y
)
+
2
b
y
d
y
d
x
=
0
⇒
d
y
d
x
=
−
a
x
+
h
y
h
x
+
b
y
⇒
[
d
y
d
x
]
P
=
−
a
h
and
[
d
y
d
x
]
a
=
−
a
h
⇒
[
d
y
d
x
]
P
=
[
d
y
d
x
]
a
Hence, the tangents are parallel.
© examsnet.com
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