parametric equation

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Parametric equation is used to define a relation with help of parameters. Parameter equation is given as: x = f (c) and y = g (c). Now we will understand how to find the second derivative of this equation. Second derivative of a parametric equation is given as:

⇒ d²y / dx² = d / dx (dy / dx), it can also be written as:

⇒ d²y / dx² = d / dc (dy / dx).dc / dx, we can also write it as:

⇒ d²y / dx² = d / dc (y / x) 1 / x;

⇒ d²y / dx² = xy – yx / x³;

Now we will understand this derivative with help of an example:

Suppose we have x (c) = 8c² and y (c) = 5c, then first derivative of this equation is given as:

⇒ [(dy / dc) / (dx / dc)] = y (c) / x (c),

Here the value of x (c) indicates the derivative of ‘x’ with respect to ‘c’. If derivative of an equation is given in this way then we will use chain rule for calculating the equation. So on moving further we get:

⇒ dy / dx = [dy / dc . dc / dx] by the definition of chain rule:

⇒ dy / dc = dy / dx . dx / dc,

Differentiate both given function with respect to’ c’ and we get:

⇒ dx / dc = 16 c and dy / dp = 5,  if we put these values in the equation then we get:

⇒ dy / dx = y / x = 5 / 16c, which is the required solution.

Median of a Triangle can be defined as a line segment which joins a vertex to the midpoint of the opposing side.

Icse 2013 solved papers can be downloaded from different websites. In the next session we will discuss about Permutation and Combination.