Question

If x and y are connected parametrically by the equation, without eliminating the parameter, find .

Answer 1

It is given that x and y are parametrically connected by the equations,

x=2a t 2 (1)

And,

y=a t 4 (2)

Differentiate both sides of equation (2) with respect to t.

dy dt =4a t 4−1 dy dt =4a t 3

Differentiate both sides of equation (1) with respect to t.

dx dt =2×2a t 2−1 dx dt =4at

We know that,

dy dx = dy dt dx dt

Substitute the value of dy dt and dx dt .

dy dx = 4a t 3 4at dy dx = t 2

Thus, the solution is dy dx = t 2 .