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Byju's Answer
Standard XII
Mathematics
Slope of a Line
C: x2+y2=9, ...
Question
C
:
x
2
+
y
2
=
9
,
E
:
x
2
9
+
y
2
4
=
1
,
L
:
y
=
2
x
Equation of the diameter of the ellipse
E
conjugate to the diameter represented by
L
is :
A
9
x
+
2
y
=
0
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B
2
x
+
9
y
=
0
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C
4
x
+
9
y
=
0
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D
4
x
−
9
y
=
0
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Solution
The correct option is
B
2
x
+
9
y
=
0
Let
y
=
m
x
be the diameter conjugate to the diameter
L
:
y
=
2
x
of the ellipse
E
then,
2
m
=
−
4
9
(
∵
m
m
′
=
−
b
2
a
2
)
⇒
m
=
−
2
9
and the equation of the conjugate diameter is
y
=
−
2
9
x
or
2
x
+
9
y
=
0
Suggest Corrections
0
Similar questions
Q.
If
y
+
3
x
=
0
is the equation of a chord of the circle,
x
2
+
y
2
–
30
x
=
0
, then the equation of the circle with this chord as diameter is
Q.
C
:
x
2
+
y
2
=
9
,
E
:
x
2
9
+
y
2
4
=
1
,
L
:
y
=
2
x
Let
L
intersect
x
=
1
at point
R
. Then which of the following is correct :
Q.
C
:
x
2
+
y
2
=
9
,
E
:
x
2
9
+
y
2
4
=
1
,
L
:
y
=
2
x
P
is a point on the circle
C
. The perpendicular
P
Q
to the major axis of the ellipse
E
meets the ellipse at
M
. Then
M
Q
P
Q
is equal to
Q.
If centre of circles
x
2
+
y
2
=
25
and
x
2
+
y
2
−
4
x
+
9
y
+
3
=
0
are the endpoints of the diameter of a circle
S
, then equation of the circle
S
is
Q.
The equation of the circle which cuts orthogonally each of the three circles given below:
x
2
+
y
2
−
2
x
+
3
y
−
7
=
0
,
x
2
+
y
2
+
5
x
−
5
y
+
9
=
0
and
x
2
+
y
2
+
7
x
−
9
y
+
29
=
0
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