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Prove that the locus of the centroid of ...

Prove that the locus of the centroid of the triangle whose vertices are `(acost ,asint),(bsint ,-bcost),` and `(1,0)` , where `t` is a parameter, is circle.

A

Statement -1 is True , Statement - 2 is true , Statement- 2 is a correct explanation for statement - 7

B

Statement-1 is True , Statement-2 is True , Statement -2 is not a correct explanation for Statement - 1 .

C

Statement-1 is True , Statement - 2 is False .

D

Statement - 1 is False , Statement -2 is True .

Text Solution

Verified by Experts

The correct Answer is:
B
Let (h , k ) be the coordinates of the centroid of the given triangle . Then ,
`3h = a cos theta + b sin theta + 1 and 3 k = a sin theta - b cos theta `
`implies (3h-1)^(2) + (3k)^(2) = a^(2) + b^(2)`
`therefore` Locus of (h , k) is `(3x - 1)^(2) + (3y)^(2) = a^(2) + b^(2)`
So , statement - 1 is true .
Statement - 2 , being a geometrical result , is also true . But , statement-2 is not a correct explanation for statement - 1 .
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