if the mid point of the line segment between the axes of a line is (p,q) the find the equation
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Explanation:
Let the coordinates of A and B be (0,y) and (x,0) respectively.
Since P(a,b) is the midpoint of AB
{
2
0+x
,
2
y+0
}=(a,b)
⇒(
2
x
,
2
y
)=(a,b)
⇒
2
x
=a and
2
y
=b
∴x=2a and y=2b
Thus the respective coordinates of A and B are (0,2b) and (2a,0)
The equation of the line passing through points (0,2b) and (2a,0) is,
⇒(y−2b)=
(2a−0)
(0−2b)
(x−0)
⇒y−2b=
2a
−2b
(x)
⇒a(y−2b)=−bx
⇒ay−2ab=−bx
⇒bx+ay=2ab
On dividing both sides by ab, we obtain
ab
bx
+
ab
ay
=
ab
2ab
⇒
a
x
+
b
y
=2
Thus equation of the line is
a
x
+
b
y
=2
Answered By
toppr
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