1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Directrix of Hyperbola
Through what ...
Question
Through what angle should the axes be rotated so that equation
a
x
2
−
2
√
3
x
y
+
7
y
2
=
10
(
x
,
y
)
may be changed to
3
x
2
+
5
y
2
=
5
(
x
1
,
y
1
)
Open in App
Solution
Solution:-
a
x
2
−
2
√
3
x
y
+
7
y
2
=
10
(
x
,
y
)
Let the axes rotated by an angle
θ
.
Let the equation after rotation be-
a
X
2
−
2
√
3
X
Y
+
7
Y
2
=
10
X
=
x
cos
θ
+
y
sin
θ
Y
=
x
sin
θ
−
y
cos
θ
∴
a
X
2
−
2
√
3
X
Y
+
7
Y
2
=
10
⇒
a
(
x
cos
θ
+
y
sin
θ
)
2
−
2
√
3
(
x
cos
θ
+
y
sin
θ
)
(
x
sin
θ
−
y
cos
θ
)
+
7
(
x
sin
θ
−
y
cos
θ
)
2
=
10
⇒
a
x
2
cos
2
θ
+
a
y
2
sin
2
θ
+
2
a
x
y
sin
θ
cos
θ
−
2
√
3
x
2
cos
θ
sin
θ
−
2
√
3
x
y
sin
2
θ
+
2
√
3
x
y
cos
2
θ
+
2
√
3
y
2
cos
θ
sin
θ
+
7
x
2
sin
2
θ
+
7
y
2
cos
2
θ
−
14
x
y
sin
θ
cos
θ
=
10
⇒
x
2
(
a
cos
2
θ
+
7
sin
2
θ
−
2
√
3
sin
θ
cos
θ
)
+
y
2
(
a
sin
2
θ
+
7
cos
2
θ
+
2
√
3
cos
θ
sin
θ
)
+
x
y
(
2
a
cos
θ
sin
θ
−
14
sin
θ
cos
θ
−
2
√
3
sin
2
θ
+
2
√
3
cos
2
θ
)
=
10
⇒
x
2
(
a
cos
2
θ
+
7
sin
2
θ
−
2
√
3
sin
θ
cos
θ
)
+
y
2
(
a
sin
2
θ
+
7
cos
2
θ
+
2
√
3
cos
θ
sin
θ
)
+
x
y
(
a
sin
2
θ
−
7
sin
2
θ
+
2
√
3
(
cos
2
θ
−
sin
2
θ
)
)
=
10
⇒
x
2
(
a
cos
2
θ
+
7
sin
2
θ
−
2
√
3
sin
θ
cos
θ
)
+
y
2
(
a
sin
2
θ
+
7
cos
2
θ
+
2
√
3
cos
θ
sin
θ
)
+
x
y
(
a
sin
2
θ
−
7
sin
2
θ
+
2
√
3
cos
2
θ
)
=
10
As in equation
3
x
2
+
5
y
2
=
5
(
x
1
,
y
1
)
Coefficient of
x
y
is 0.
∴
a
sin
2
θ
−
7
sin
2
θ
+
2
√
3
cos
2
θ
=
0
⇒
sin
2
θ
(
a
−
7
)
=
−
2
√
3
cos
2
θ
⇒
tan
2
θ
=
−
2
√
3
a
−
7
⇒
θ
=
tan
−
1
(
−
2
√
3
a
−
7
)
2
Suggest Corrections
0
Similar questions
Q.
The equation of a pair of straight lines is
a
x
2
+
2
h
x
y
+
b
y
2
=
0
. By what angle must the axes be rotated so that the term containing
x
y
in the equation may be removed?
Q.
The transformed equation of
9
x
2
+
2
√
3
x
y
+
7
y
2
=
10
when the axes are rotated through an angle of
π
6
(in the anti clockwise direction) is
Q.
The angle of rotation of the axes so that the equation
a
x
+
b
y
+
c
=
0
may be reduced to
X
=
p
is
Q.
The transformed equation of
3
x
2
+
4
x
y
−
7
y
2
−
14
=
0
when origin is shifted to the point
(
−
1
,
2
)
, and then axes being rotated at an angle of
90
∘
is
Q.
The angle of rotation of the axes so that the equation
√
3
x
−
y
+
5
=
0
may be reduced to the form
Y
=
k
, where
k
is a constant is
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Hyperbola and Terminologies
MATHEMATICS
Watch in App
Explore more
Directrix of Hyperbola
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app