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TS EAMCET · Maths · Straight Lines

A rod of length 6 units slides with its ends on the coordinate axes. The locus of the midpoint of the rod is

  1. A x2+y2=9
  2. B x+y=3
  3. C x2+y2=36
  4. D x+y=6
Verified Solution

Answer & Solution

Correct Answer

(A) x2+y2=9

Step-by-step Solution

Detailed explanation

Let Aa,0 & B0,b are the end points of the rod and Ph,k be the mid-point. So, a2=h & b2=k ⇒a=2h & b=2k Length of the rod is given 6 units ⇒0-a2+b-02=6 ⇒a2+b2=62 ⇒2h2+2k2=62 ⇒4h2+4k2=36 So, locus of P is…