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 ______.

विकल्प

• (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

Answer 1

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