CircleHard

Question

B and C are fixed points having co-ordinates (3, 0) and (-3, 0) respectively. If the vertical angle ᐃBAC is 90o then the locus of the centroid of the ABC has the equation -

Options

A.x2 + y2 = 1
B.x2 + y2 = 2
C.9(x2 + y2) = 1
D.9(x2 + y2) = 4

Solution


∠ BAC = 90o    ⇒ = - 1
⇒ b2 = -(a2 - 9)  ⇒  a2 + b2 = 9            .......(i)
Now BG : GD = 2 : 1
⇒    3h = + 1 × - 3     ⇒   a = 3h
&    3k = 2 × + 1  0        b = 3k
substitute value of a & b in equation (i)
9h2 + 9k2 = 9   ⇒   x2 + y2 = 1

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