Eliminate the parameter to describe the path of the bug in t

Eliminate the parameter to describe the path of the bug in the plane for z = 2e/2 and 3-4 Select one: 0 a. The path is a parabola of equation y-z2, with z > 0 b The path is a line of equation y = 4z C. The path is a parabola of equation y d. The path is a line of equation y = z 2x2 O

Solution

x = 2e^t/2 .........(1)  and

y = 4e^t ........(2)

now we have to eliminate t from both equation so

x = 2e^{t / 2}

take square of both sides

x² = 4e^{(t / 2) * 2}

x² = 4e^t ......(3)

compare equation (2) and (3) we get

x² = y

y = x² and this is a equation of parabola.

ans option(a).