COMEDK Exam 2019 Solved Paper

We have, equation of line ‌

x

a

+‌

y

b

=1.
Let P(h,k) be the required point.
Now, coordinates A and B are (a,0) and (0,b) respectively. Since, P is mid-point of AB.
Therefore,
(h,k)‌=(‌

a+0

2

,‌

0+b

2

)
⇒‌‌h‌=‌

a

2

‌ and ‌k=‌

b

2

⇒‌‌a‌=2h‌ and ‌b=2k
Now, it is given that
‌a+b=4
⇒‌2h+2k=4
⇒‌h+k=2
So, locus of P is x+y=2