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Question

If A(4,3),B(0,2) and points B lies on the locus Y=1+x2, find the equation of the locus of the centroid of ABC.

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Solution

Let the coordinate of c be (a, b) and the coordinates of the centroid of the triangle ABC be (h, k) then,
(h,k)=(5+2+a3,2+4+b3)
(h,k)=(a+73,b+23)
h=a+73
h2=(a+73)2
9h2=a2+14a+49 ……(1)
k=b+23
k2=(b+23)2
9k2=b2+4b+4 ………(2)
Adding (1) and (2)
9h2+9k2=a2+14a+49+b2+4b+4
9h2+9k2=a2+b2+14a+4b+53
Replacing h and k by x and y we get
9x2+9y2=a2+b2+14a+4b+53 is the required equation.

1188020_1242264_ans_ad6b281ec8394d6898868d67c08d5799.jpg

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