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Byju's Answer
Standard XII
Mathematics
Equation of Family of Circles Touching a Line and Passing through a Given Point on the Line
solve a) ...
Question
solve
a
)
F
i
n
d
t
h
e
p
o
i
n
t
s
o
n
t
h
e
c
u
r
v
e
y
=
x
3
-
10
x
+
8
a
t
w
h
i
c
h
t
h
e
tan
g
e
n
t
i
s
p
a
r
a
l
l
e
l
t
o
t
h
e
l
i
n
e
y
=
2
x
+
1
b
)
I
s
t
h
e
g
i
v
e
n
l
i
n
e
y
=
2
x
+
1
tan
g
e
n
t
t
o
t
h
e
c
u
r
v
e
?
W
h
y
?
Open in App
Solution
Dear student
Let
P
x
1
,
y
1
be
the
required
point
.
The
given
curve
is
y
=
x
3
-
10
x
+
8
.
.
.
1
⇒
dy
dx
=
3
x
2
-
10
⇒
dy
dx
x
1
,
y
1
=
3
x
1
2
-
10
Since
the
tangent
at
x
1
,
y
1
is
parallel
to
the
line
y
=
2
x
+
1
So
,
slope
of
tangent
at
x
1
,
y
1
=
slope
of
the
line
y
=
2
x
+
1
⇒
dy
dx
x
1
,
y
1
=
2
∵
y
=
mx
+
c
has
slope
m
,
so
y
=
2
x
+
1
has
slope
2
⇒
3
x
1
2
-
10
=
2
⇒
3
x
1
2
=
12
⇒
x
1
2
=
4
⇒
x
1
=
±
2
Since
x
1
,
y
1
lies
on
the
curve
1
,
So
,
y
1
=
x
1
3
-
10
x
1
+
8
Now
,
when
x
1
=
2
⇒
y
1
=
2
3
-
10
2
+
8
=
-
4
When
x
1
=
-
2
⇒
y
1
=
-
2
3
-
10
-
2
+
8
=
-
8
+
20
+
8
=
20
Thus
the
required
points
are
2
,
-
4
and
-
2
,
20
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Equation of Family of Circles Touching a Line and Passing through a Given Point on the Line
Standard XII Mathematics
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