NIMCET 2018 Question Paper with solutions

Let the equation of line having intercept a, b, on coordinates axes is
$\frac{\mathit{x}}{\mathit{a}}+\frac{\mathit{y}}{\mathit{b}}$ = 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)
∴ $\frac{4}{\mathit{a}}+\frac{2}{\mathit{b}}$ = 1 ... (ii)

Since, (h,k) is circumcentre of Δ OPQ. Therefore (h,k) is the mid point of PQ
∴ h = $\frac{0+\mathit{a}}{2}$ = $\frac{\mathit{a}}{2}$ and k = $\frac{0+\mathit{b}}{2}$ = $\frac{\mathit{b}}{2}$ ... (iii)
⇒ a = 2h and b = 2k
∴ From Eq. (ii) and Eq. (iii), we get
$\frac{4}{2\mathit{h}}+\frac{2}{2\mathit{k}}$ = 1
⇒ $\frac{2}{\mathit{h}}+\frac{1}{\mathit{k}}$ = 1
∴ Locus of the circumcentre is $\frac{2}{\mathit{a}}+\frac{1}{\mathit{y}}$ = 1