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

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 (A) 1 (B) 3 (C) 5 (D) 11

Tardigrade Admin · Accepted Answer

Sum of distances will be minimum if P, (8,0) and (0,12) will collinear ∴ (x/8)+(y/12)=1 ⇒ y=12-(3/2)x ∴ (x, y)≡(2, 9), (4, 6), (6, 3)

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

$1$

$3$

$5$

$11$

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

Q. 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

1

3

5

11

Sum of distances will be minimum if P, (8,0) and (0,12) will collinear ∴8x​+12y​=1⇒y=12−23​x ∴(x,y)≡(2,9),(4,6),(6,3)

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

$1$

$3$

$5$

$11$

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