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AP EAMCET Engineering 21 Sep 2020 Shift 2 Paper
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© examsnet.com
Question : 35
Total: 160
Find the condition for the line
a
x
+
b
y
+
c
=
0
to be a normal to an ellipse
x
2
4
+
y
2
36
=
1
1
a
2
+
1
b
2
=
144
c
2
1
a
2
+
1
b
2
=
128
c
2
1
a
2
+
9
b
2
=
256
c
2
1
a
2
+
9
b
2
=
32
c
2
Validate
Solution:
(c) Let a point
P
(
2
cos
θ
,
6
sin
θ
)
on the ellipse
x
2
4
+
y
2
36
=
1
,
so equation of normal to the ellipse at point
P
is
x
−
2
cos
θ
cos
θ
2
=
y
−
6
sin
θ
sin
θ
6
⇒
2
x
sec
θ
−
4
=
6
y
c
o
s
e
c
θ
−
36
⇒
2
x
sec
θ
−
6
y
c
o
s
e
c
θ
+
32
=
0
.
.
.
.
.
(
i
)
Let normal (i) represent the line
a
x
+
b
y
+
c
=
0
So
a
2
sec
θ
=
b
−
6
c
o
s
e
c
θ
=
c
32
⇒
cos
θ
=
c
16
a
,
sin
θ
=
−
3
c
16
b
∵
cos
2
θ
+
sin
2
θ
=
1
⇒
c
2
256
a
2
+
9
c
2
256
b
2
=
1
⇒
1
a
2
+
9
b
2
=
256
c
2
© examsnet.com
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