Question

if points (a,0), (0,b), (1, 1) are collinear then prove that 1/a+1/b =1 or a+b =ab​

Answer 1

Answer:

Given points are (a,0),(0,b) and (1,1)

x

1

=a,y

1

=0,x

2

=0,y

2

=b and x−3=1,y

3

=1

Condition for collinearity

x

1

y

2

+x

2

y

3

+x

3

y

1

=x 2y 1 +x 3

y2+x 1

y 3

gives

ab+0+0=0+1.b+a.1⇒ab=a+b

⇒1= b1 + a1

⇒ a1 + b 1 =1

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