1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Formation of a Differential Equation from a General Solution
Find the equa...
Question
Find the equation of the circle passing through point of intersection of the circle
x
2
+
y
2
−
8
x
−
2
y
+
7
=
0
and
x
2
+
y
2
−
4
x
+
10
y
+
8
=
0
and its center lie on y-axis.
Open in App
Solution
The equation of a circle passing through the point of intersection of the given circles is
x
2
+
y
2
−
8
x
−
2
y
+
7
+
4
(
x
2
+
y
2
−
4
x
+
10
y
+
15
)
=
0
Where
h
is as arbitary constant
or
(
1
+
k
)
x
2
+
(
1
+
k
)
y
2
−
4
x
(
2
+
k
)
−
2
y
(
1
−
5
k
)
+
7
+
8
k
=
0
or
x
2
+
y
2
−
4
(
2
+
k
1
+
k
)
x
−
2
(
1
−
5
k
1
+
k
)
y
+
7
+
8
k
1
+
k
=
0
where
k
≠
−
1
The coordinates of center of circle is
{
−
2
(
2
+
k
)
(
1
+
k
)
−
(
1
−
5
k
)
(
1
+
k
)
}
Since center of the circle lies on
y
−
axis.
Abscissa
=
0
−
2
(
2
+
k
1
+
k
)
=
0
⇒
k
=
−
2
From
(
1
)
equation of required circle
x
2
+
y
2
−
8
x
−
2
y
+
2
(
x
2
+
y
2
−
4
x
+
10
y
+
8
)
=
0
x
2
+
y
2
+
22
y
+
9
=
0
Suggest Corrections
0
Similar questions
Q.
The equation of the circle which passes through the point of intersection of circles
x
2
+
y
2
−
8
x
−
2
y
+
7
=
0
and
x
2
+
y
2
−
4
x
+
10
y
+
8
=
0
and having its centre on
y
−
axis, will be
Q.
The equation of the circle concentric with the circle
x
2
+
y
2
+
8
x
+
10
y
−
7
=
0
and passing through the centre of the circle
x
2
+
y
2
−
4
x
−
6
y
=
0
is
Q.
Find the equation of the circle passing through the points of intersection of the circle
x
2
+
y
2
−
6
x
+
2
y
+
4
=
0
and
x
2
+
y
2
+
2
x
−
4
y
−
6
=
0
and with its centre on the line
y
=
x
Q.
The equation of the circle concentric with the circle
x
2
+
y
2
+
8
x
+
10
y
−
7
=
0
and passing through the centre of the circle
x
2
+
y
2
−
4
x
−
6
y
=
0
is-
Q.
The equation of the circle having the center on the line
x
+
2
y
−
3
=
0
and passing through the points of intersection of the circles
x
2
+
y
2
−
2
x
−
4
y
+
1
=
0
and
x
2
+
y
2
−
4
x
−
2
y
+
4
=
0
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
Formation of Differential Equation
MATHEMATICS
Watch in App
Explore more
Formation of a Differential Equation from a General Solution
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