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Question
Locus of centroid of the triangle whose vertices are (a cos t, a sin t),(b sin t, – b cos t) and (1, 0), where t is a parameter is ______.
Options
(3x + 1)2 + (3y)2 = a2 – b2
(3x – 1)2 + (3y)2 = a2 – b2
(3x – 1)2 + (3y)2 = a2 + b2
(3x – 1)2 + (3y)2 = a2 + b2
MCQ
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Solution
Locus of centroid of the triangle whose vertices are (a cos t, a sin t),(b sin t, – b cos t) and (1, 0), where t is a parameter is `underlinebb((3x - 1)^2 + (3y)^2 = a^2 + b^2)`.
Explanation:
We know that centroid
(x, y) = `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`
x = `(a cos t + b sin t + 1)/3`
⇒ a cos t + b sin t = 3x – 1
y = `(a sin t - b cos t)/3`
⇒ a sin t – b cos t = 3y
Squaring and adding,
(3x – 1)2 + (3y)2 = a2 + b2
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Locus
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