Manipal Entrance Test 2013 Math Paper

Let the equation of the line be

x

a

+

y

b

=1 ......(i)
Its intercepts on y and x axes are b and a respectively.
According to the question,

1

a

+

1

b

= constant =K (say)
∴

1

aK

+

1

bK

=1
⇒

1∕K

a

+

1∕K

b

=1 ....(ii)
From (ii) it follows that line (i) passes through the fixed point (

1

K

,

1

K

).