NIMCET 2018 Question Paper with solutions

Let the equation of line having intercept a, b, on coordinates axes is

x

a

+

y

b

= 1 ... (i)
∴ This intercept line meet the coordinate axes at P(a,0) and Q (0, b), respectively
Since, Eq. (i) passes through (4, 2)
∴

4

a

+

2

b

= 1 ... (ii)

Since, (h,k) is circumcentre of Δ OPQ. Therefore (h,k) is the mid point of PQ
∴ h =

0+a

2

=

a

2

and k =

0+b

2

=

b

2

... (iii)
⇒ a = 2h and b = 2k
∴ From Eq. (ii) and Eq. (iii), we get

4

2h

+

2

2k

= 1
⇒

2

h

+

1

k

= 1
∴ Locus of the circumcentre is

2

a

+

1

y

= 1