Question

prove that the points (a,0) , (0,b) and (1,1) are collinear of 1/a plus 1/b=1

Answer 1

the line joining (a,0) ,(0,b)
is y/b+x/a=1
if (1,1) satisfies it then it will be collinear to it

Answer 2

(a,0), (0,b) and (1,1) are collinear if

a

1

​

+

b

1

​

=1

proof

Use area of triangle formed by using those points is equal to zero

Area of triangle =

2

1

​

[a(b−1)+0+1(0−b)]

0=ab−a−b

a+b=ab

Divide both sides by ab

ab

a

​

+

ab

b

​

=1

b

1

​

+

a

1

​

=1

Hence proved.