1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
11
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B 3As we know, distance is minimum, if points are collinear ∴(x,y),(8,0),(0,12) are collinear x(−12)+8(12−y)=0 ⇒−12x+96−8y=0 ⇒3x+2y−24=0 ⇒y=12−32x As x and y are natural number. Thus, possibles solutions are (2,9),(4,6),(6,3) ∴ 3 points are possible.

Suggest Corrections
2
Join BYJU'S Learning Program
Related Videos
Perpendicular Distance of a Point from a Plane
MATHEMATICS
Watch in App
Join BYJU'S Learning Program