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Byju's Answer
Standard IX
Mathematics
Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.
P: x2-y2+2y-1...
Question
P
:
x
2
−
y
2
+
2
y
−
1
=
0
L
:
x
+
y
=
3
Equation of the angle bisectors of the pairs of lines P is
A
x
y
−
y
=
0
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B
x
y
−
x
=
0
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C
x
y
=
0
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D
x
y
+
y
=
0
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Solution
The correct option is
C
x
y
−
x
=
0
P
:
x
2
−
(
y
−
1
)
2
=
0
⇒
x
+
y
−
1
=
0
and
x
−
y
+
1
=
0
Equation of the angle bisector is
A
1
x
+
B
1
y
+
C
1
√
A
2
1
+
B
2
1
=
±
A
2
x
+
B
2
y
+
C
2
√
A
2
2
+
B
2
2
x
+
y
−
1
√
2
=
±
x
−
y
+
1
√
2
⇒
x
=
0
or
y
−
1
=
0
Suggest Corrections
0
Similar questions
Q.
P
:
x
2
−
y
2
+
2
y
−
1
=
0
L
:
x
+
y
=
3
Area of the triangle formed by the angle bisectors of the pair of lines
P
and the line
L
(in square units) is
Q.
Find what the following equations become when the origin is shifted to the point
(
1
,
1
)
?
(i)
x
2
+
x
y
−
3
x
−
y
+
2
=
0
(ii)
x
2
−
y
2
−
2
x
+
2
y
=
0
(iii)
x
y
−
x
−
y
+
1
=
0
(iv)
x
y
−
y
2
−
x
+
y
=
0
Q.
Solve the following pair of equations.
7
x
−
2
y
x
y
=
5
8
x
+
6
y
x
y
=
15
Here, x
≠
0 and y
≠
0.
Q.
Assertion :If the two pair of lines
x
2
−
2
m
x
y
−
y
2
=
0
and
x
2
−
2
n
x
y
−
y
2
=
0
are such that one of them represents the bisector of angle between the other, then
1
+
m
n
=
0
. Reason: Equation of bisector of angle between the pair of lines
a
x
2
+
2
h
x
y
+
b
y
2
=
0
is given by
x
2
−
y
2
a
−
b
=
x
y
h
.
Q.
P
:
x
2
−
y
2
+
2
y
−
1
=
0
L
:
x
+
y
=
3
Combined equation of L and L' is:
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