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AP EAMCET2012MathematicsStraight Lines

A point moves in the x y -plane such that the sum of its distance from two mutually perpendicular lines is always equal to 5 units. The area (in sq units) enclosed by the locus of the point, is

Options

  1. A25 4
  2. B25
  3. C50
  4. D100

Correct answer

C. 50

Step-by-step solution

In a figure, x x^ and y y^ are two perpendicular axes. |x|+|y|=5 Coordinates of B and C are (5,0) and (0,5) . Length of B C= 5^2+5^2 =5 2 Area of square A B C D=(5 2 )^2=50

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