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BITSAT2016MathematicsCircleActual

The line joining (5,0) to ((10 , 10 ) is divided internally in the ratio 2: 3 at P . If varies, then the locus of P is

Options

  1. Aa pair of straight lines
  2. Ba circle
  3. Ca straight line
  4. DNone of these

Correct answer

B. a circle

Step-by-step solution

Let P ( x , y ) be the point dividing the join of A and B in the ratio 2: 3 internally, then array c x = 20 +15 5 =4 +3 = x -3 4 y = 20 +0 5 =4 = y 4 (ii) array Squaring and adding (i) and (ii), we get the required locus (x-3)²+y²=16, which is a circle.

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