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For points P-=(x1,y1) and Q-=(x2,y2) of ...

For points `P-=(x_1,y_1)` and `Q-=(x_2,y_2)` of the coordinates plane, a new distance d (P,Q) is defined by `d(P,Q) =|x_1-x_2|+|y_1-y_2|`. Let `O-=(0,0)` and `A-=(3,2)`. Consider the set of points P in the first quadrant which are equidistant (with respect to the new distance) from O and A.
The area of the ragion bounded by the locus of P and the line `y=4` in the first quadrant is

A

2sq.units

B

4 sq.units

C

6 sq.units

D

noen of these

Text Solution

Verified by Experts

The correct Answer is:
B

Area of region `OBCDEFO`
`A="Area of trapezium" OBCF+"Area of rectangle"FCDE`
`=(1)/(2)xx((5)/(2)+(1)/(2))xx2+(1)/(2)xx2`
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