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Byju's Answer
Standard XII
Mathematics
Linear Equation
Every equatio...
Question
Every equation of form ax + by + c = 0 represents a line in xy plane. where
a
2
+
b
2
≠
0
A
True
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B
False
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Solution
The correct option is
A
True
Suggest Corrections
0
Similar questions
Q.
Assertion :The two straight lines given by the equation
(
a
2
−
3
b
2
)
x
2
+
8
a
b
x
y
+
(
b
2
−
3
a
2
)
y
2
=
0
from with the line
a
x
+
b
y
+
c
=
0
a triangle of area
c
2
√
3
(
a
2
+
b
2
)
Reason: The triangles formed by the lines
(
a
2
−
3
b
2
)
x
2
+
8
a
b
x
y
+
(
b
2
−
3
a
2
)
y
2
=
0
and
a
x
+
b
y
+
c
=
0
is an equilateral triangle.
Q.
Let
a
,
b
,
c
be real numbers with
a
2
+
b
2
+
c
2
=
1
.
show that the equation
∣
∣ ∣
∣
a
x
−
b
y
−
c
b
x
+
a
y
c
x
+
a
b
x
+
a
y
−
a
x
+
b
y
−
c
c
y
+
b
c
x
+
a
c
y
+
b
−
a
x
−
b
y
+
c
∣
∣ ∣
∣
=
0
represents a straight line.
Q.
Show that the straight lines
(
A
2
−
3
B
2
)
x
2
+
8
A
B
x
y
+
(
B
2
−
3
A
2
)
y
2
=
0
form with the line
A
x
+
B
y
+
C
=
0
an equilateral triangle of area
C
2
√
3.
(
A
2
+
B
2
)
.
Q.
I : Every first degree equation in
x
and
y
is
a
x
+
b
y
+
c
=
0
,
|
a
|
+
|
b
|
≠
0
represents a straight line.
II : Every first degree equation in
x
and
y
can be converted into slope-intercept form.
Then which of the above statements are true?
Q.
Let
a
,
b
,
c
be real numbers with
a
2
+
b
2
+
c
2
=
1
Show that the equation
∣
∣ ∣
∣
a
x
−
b
y
−
c
b
x
+
a
y
c
x
+
a
b
x
+
a
y
−
a
x
+
b
y
−
c
c
y
+
b
c
x
+
a
c
y
+
b
−
a
x
−
b
y
+
c
∣
∣ ∣
∣
= 0
represents a straight line.
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