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Byju's Answer
Standard XII
Mathematics
Equation of Tangent in Point Form
If tangent to...
Question
If tangent to the circle
x
2
+
y
2
=
5
at
(
1
,
−
2
)
also touches the circle
x
2
+
y
2
−
8
x
+
6
y
+
20
=
0
at point
(
h
,
k
)
,
then the value of
h
+
k
is
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Solution
S
1
:
x
2
+
y
2
=
5
S
2
:
x
2
+
y
2
−
8
x
+
6
y
+
20
=
0
Equation of tangent at
(
1
,
−
2
)
to
S
1
is
x
−
2
y
−
5
=
0
Put
x
=
2
y
+
5
in
S
2
,
we get
(
2
y
+
5
)
2
+
y
2
−
8
(
2
y
+
5
)
+
6
y
+
20
=
0
⇒
5
y
2
+
10
y
+
5
=
0
⇒
(
y
+
1
)
2
=
0
⇒
y
=
−
1
⇒
x
=
−
2
+
5
=
3
So, point of contact is
(
3
,
−
1
)
.
∴
h
+
k
=
2
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0
Similar questions
Q.
If tangent to the circle
x
2
+
y
2
=
5
at
(
1
,
−
2
)
also touches the circle
x
2
+
y
2
−
8
x
+
6
y
+
20
=
0
at point
(
h
,
k
)
,
then the value of
h
+
k
is
Q.
If the tangent to the circle
x
2
+
y
2
=
5
at the point
(
1
,
−
2
)
also touches the circle
x
2
+
y
2
−
8
x
+
6
y
+
20
=
0
, then its point of contact is
Q.
Tangent to circle
x
2
+
y
2
=
5
at
(
1
,
−
2
)
also touches the circle
x
2
+
y
2
−
8
x
+
6
y
+
20
=
0
. Co-ordinate of the corresponding point of contact, is
Q.
The tangent to the circle
x
2
+
y
2
=
5
at the point
(
1
,
−
2
)
also touches the circle
x
2
+
y
2
−
8
x
+
6
y
+
20
=
0
at
Q.
Prove that the tangent to the circle
x
2
+
y
2
=
5
at the point
(
1
,
−
2
)
also touches the circle
x
2
+
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−
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+
6
y
+
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and find its point of contact.
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