1. Tardigrade
  2. Question
  3. Mathematics
  4. Let S be the set of points whose abscissas and ordinates are natural numbers. Let P ∈ S such that the sum of the distance of P from (8,0) and (0,12) is minimum among all elements in S. Then the number of such points P in S is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $S$ be the set of points whose abscissas and ordinates are natural numbers. Let $P \,\in\, S$ such that the sum of the distance of $P$ from $(8,0)$ and $(0,12)$ is minimum among all elements in $S$. Then the number of such points $P$ in $S$ is

WBJEEWBJEE 2016Straight Lines

Solution:

Sum of distances will be minimum if P, (8,0) and $(0,12)$ will collinear
$\therefore \frac{x}{8}+\frac{y}{12}=1 \Rightarrow y=12-\frac{3}{2}x$
$\therefore \left(x, y\right)\equiv\left(2, 9\right), \left(4, 6\right), \left(6, 3\right)$