Question

What will be the value of the co-ordinate whose position of a particle moving along the parabola y^2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?

(a) (1, 1)

(b) (2, 2)

(c) (3, 3)

(d) (4, 4)

I have been asked this question during an online interview.

The above asked question is from Application of Derivative topic in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

Correct option is (d) (4, 4)

The best explanation: Here, y^2 = 4x ……….(1)

Let, (x, y) be the position of the particle moving along the parabola (1) at time t.

Now, differentiating both sides of (1) with respect to t, we get:

2y(dy/dt) = 4(dx/dt)

Or, y(dy/dt) = 2(dy/dt) ……….(2)

By question, dx/dt = 2 * dy/dt ……….(3)

From (2) and (3) we get, y(dy/dt) = 2 * 2 dy/dt

Or, y = 4

Putting y = 4 in (1) we get, 4^2 = 4x

So, x = 4

Thus, the co-ordinate of the particle is (4, 4).