Question

Locus of centroid of the triangle whose vertices are $(a\cos t,a\sin t),\mspace{6mu}(b\sin t, - b\cos t)$ and (1, 0), where t is a

parameter; is.

• A. $(3x - 1)^{2} + (3y)^{2} = a^{2} - b^{2}$
• B. $(3x - 1)^{2} + (3y)^{2} = a^{2} + b^{2}$
• C. $(3x + 1)^{2} + (3y)^{2} = a^{2} + b^{2}$
• D. $(3x + 1)^{2} + (3y)^{2} = a^{2} - b^{2}$

Answer 1

Answer: (B)

$(3x - 1)^{2} + (3y)^{2} = a^{2} + b^{2}$

Answer 2

$3 h = a \cos t + b \sin t + 1,3 k = a \sin t - b \cos t$

$a ^ { 2 } + b ^ { 2 } = ( 3 h - 1 ) ^ { 2 } + ( 3 k ) ^ { 2 }$

$( 3 x - 1 ) ^ { 2 } + ( 3 y ) ^ { 2 } = a ^ { 2 } + b ^ { 2 }$.