Question

if the point (a,0),(0,b)&(1,1)are collinear,then prove that 1/a+1/b=1​

Answer 1

Let,A=(a,0)

B=(0,b)

C=(1,1)

since,given points are collinear

slope of AB=slope of BC

b-0/0-a=1-b/1-0

b/-a=1-b/1

b=-a+AB

b=a(b-1)

a=b/b-1

given equation,

1/a+1/b=1

L.H.S=1/a+1/b

=1/(b/b-1)+1/b

=b-1/b+1/b

=b-1+1/b

=b/b

=1

=R.H.S

hence proved.