1.

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» 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).


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