Find the locus of the centroid of a triangle whose vertices are (a cos t, a sin t),
(b sin t, –b cos t) and
(1, 0) where ‘t’ is the parameter.

Question

Find the locus of the centroid of a triangle whose vertices are (a cos t, a sin t), (b sin t, –b cos t) and (1, 0) where ‘t’ is the parameter.

Ravi · Answer

Use the formula for the coordinates of the centroid as

x=(x1+x2+x3)/3 , y= (y1+y2+y3)/3

where (x1, y1), (x2, y2) and (x3,y3) are vertices of the triangle.

Use the relation for the coordinates x and y in terms of t to form the equation. If no information further in context to t is given, you can substitute the trig ratios x equality to y equality to form the equation.

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Find the locus of the centroid of a triangle whose vertices are (a cos t, a sin t), (b sin t, –b cos t) and (1, 0) where ‘t’ is the parameter.

Find the locus of the centroid of a triangle whose vertices are (a cos t, a sin t),
(b sin t, –b cos t) and
(1, 0) where ‘t’ is the parameter.

1 Answers

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Find the locus of the centroid of a triangle whose vertices are (a cos t, a sin t), (b sin t, –b cos t) and (1, 0) where ‘t’ is the parameter.

Find the locus of the centroid of a triangle whose vertices are (a cos t, a sin t),(b sin t, –b cos t) and(1, 0) where ‘t’ is the parameter.

1 Answers

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Find the locus of the centroid of a triangle whose vertices are (a cos t, a sin t),
(b sin t, –b cos t) and
(1, 0) where ‘t’ is the parameter.