Question

If points (a,0) , (0,b)(0,b)  and (1,1)  are collinear, then 1/a+1/b=​

Answer 1

Answer:

Given that three points are collinear, (a,o),(o,b) and (1,1)

Since the points are collinear, area of triangle formed by these points is equal to O.

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]=0

2

1

[a[b−1]+0[1−0]+1(0−b)]=0

⇒ab−a−b=0

⇒a+b=ab

∴

a

1

+

b

1

=1

Answer 2

$\huge \mathbb \red{ANSWER : }$

Let A a,0, B0,b and C1,1

the point

∴ points A,B,C are collinear

∴ slop of AB =slop of AC

$\sf \frac{b - 0}{0-a} = \frac{1 = 0}{1-a}$

$\sf = \sf - \frac{ b}{a} = \frac{1}{1 - a}$

$\sf = - b+ab = a$

$\sf{a + b = ab}$

$\sf \frac{a}{ab} + \frac{b}{ab} =1$

$\sf \frac{1}{b} + \frac{1}{a} = 1$

$\small \sf \color{lime} \boxed{hope \: it \: helpes \: you : )}$