Straight Line Question 271

Question: The area of the region bounded by the locus of a point P satisfying $ d(P,A)=4 $ , where A is (1, 2) is

Options:

A) 64 sq. unit

B) 54 sq. unit

C) $ 16\pi sq.unit $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • [a] We have, max $ { |x-1|, |y-2| } = 4 $ If $ { |x-1| \ge |y-2| }, $ then $ | x-1 |=4, $ i.e., if $ (x+y-3)(x-y+1)\ge 0, $ Then $ x = -3 \text{ or } 5, $ If $ | y-2 |\ge | x-1 |, $ Then $ | y-2 |=4 $ i.e., $ (x+y-3)(x-y+1)\le 0, $ Then $ y = -2 \text{ or } 6 $. So, the locus of P bounds a square, the equation of whose sides are $ x=-3,x=5,y=-2,y=6 $ Thus, the area is $ {{(8)}^{2}}=64. $

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