If p (x, y) is any point on the line joining the
points A (a,0) and B (0, b), then show that x/a +
y/b = 1
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Answer:
If a point (x,y) lies on a line joining the points A(x
1
,y
1
) and B(x
2
,y
2
), the equation of the line is given by
⇒
x−x
1
y−y
1
=
x
2
−x
1
y
2
−y
1
Point P(x,y) lies on the line joining the points A(a,0) and B(0,b). So,
⇒
x−a
y−0
=
0−a
b−0
⇒
x−a
y
=
a
−b
⇒ ay=−b(x−a)
⇒ ay=−bx+ab
⇒ ay+bx=ab
Divide both sides by ab
⇒
ab
ay
+
ab
bx
=
ab
ab
⇒
b
y
+
a
x
=1 ----- Hence proved
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