Binomial Theorem


If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus. 


A parabolic reflection with diameter PR = 20 cm and OQ = 5 cm is shown below:
Here, vertex of the parabola is (0, 0)
Let the focus be S (a, 0)
Let the equation of the parabola be straight y squared equals 4 ax.
Now,     PR = 20 cm rightwards double arrow PQ = 10 cm
Also,                   OQ = 5 cm
∴   Point P is (5, 10)
Since it lies on the parabola straight y squared equals 4 ax
∴   10 squared space equals 4 space left parenthesis straight a right parenthesis space 5 space rightwards double arrow space 100 space equals space 20 straight a space rightwards double arrow space straight a space equals space 5
∴    Focus is S (5, 0) which is same as point Q.

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