A straight line forms a triangle of area 24 sq unit with the coordinate axes such that quadrant. Find
equation of the line if it passes through (3, 4)
[Ans: 4x + 3y - 24 = 0)
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Given that,
Area of triangle =24squnits
We know that,
Equation of line in intercept form
a
x
+
b
y
=1
If it passes through (3,4)
Then,
a
3
+
b
4
=1
4a+5b=ab........(1)
Given that
Area of triangle
=
2
1
ab
2
1
ab=24
ab=48
b=
a
48
.......(2)
Put the equation (1) and we get,
4a+3(
a
48
)=48
4a
2
+3×48=48a
4a
2
−48a+3×48=0
4(a
2
−12a+3×12)=0
a
2
−12a+36=0
(a−6)
2
=0
a=6
Then, put the value of a=6 in equation (2)
ab=48
6b=48
b=8
Hence, the equation of line is
a
x
+
b
y
=1
6
x
+
8
y
=1
Hence, this is the answer.
Area of triangle =24squnits
We know that,
Equation of line in intercept form
a
x
+
b
y
=1
If it passes through (3,4)
Then,
a
3
+
b
4
=1
4a+5b=ab........(1)
Given that
Area of triangle
=
2
1
ab
2
1
ab=24
ab=48
b=
a
48
.......(2)
Put the equation (1) and we get,
4a+3(
a
48
)=48
4a
2
+3×48=48a
4a
2
−48a+3×48=0
4(a
2
−12a+3×12)=0
a
2
−12a+36=0
(a−6)
2
=0
a=6
Then, put the value of a=6 in equation (2)
ab=48
6b=48
b=8
Hence, the equation of line is
a
x
+
b
y
=1
6
x
+
8
y
=1
Hence, this is the answer.
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