Describe the motion of a particle with position (x, y) as t varies in the given

Question

Describe the motion of a particle with position (x, y) as t varies in the given interval x = 8t - 3, y = 2 - t, lessthanorequalto t lessthanorequalto 1 Also write the Cartesian equation. a. particle moves along the circle from (-3, 2) (5, 1). (x + 3)^2 + (y - 2)^2 = 13 b. particle moves along the ellipse from (-3, 2) (5, 1). (x + 3)^2/25 + (y - 2)^2/1 = 1 c. particle moves long the hyperbola from (-3, 2) (5, 1). (x + 3)^2/25 - (y - 2)^1/2/1 = 1 d. particle moves along the line from (-3, 2) (5, 1). x + 8y = 13 e. none of these

Explanation / Answer

x=8t-3,

when t=0, x=0-3=-3

when t=1, x=8-3=5

y=2-t

when t=0, y=2

when t=1, y=2-1=1

now,

x=8t-3...............eq (1)

y=2-t

t=2-y

so eq(1) becomes,

x=8(2-y)-3

x=16-8y-3

x+8y=13

so answer is (d)

Particle moves along the line from (-3,2) (2,1) along the line x+8y=13.

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