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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

For a ∆ A B C , if B ≡ 3 , 0 , C ≡ - 3 , 0 and the angle B A C is 90 ° , then the locus of the centroid of the triangle is

Options

  1. Ax 2 + y 2 = 1
  2. Bx 2 + y 2 = 2
  3. C9 x 2 + y 2 = 1
  4. D9 x 2 + y 2 = 4

Correct answer

A. x 2 + y 2 = 1

Step-by-step solution

Let, A a , b and G h , k . Now, A , G , O are collinear ⇒ h = 2.0 + a 3 ⇒ a = 3 h and similarily b = 3 k . Now, a , b lies on the circle x 2 + y 2 = 9 ⇒ a 2 + b 2 = 1 Hence, locus of the centroid is x 2 + y 2 = 1

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