Binomial Theorem

Question
CBSEENMA11015114

In the following, find the co-ordinates of the focus, axis of the parabola, the equation of the directrix and length of the latus rectum.
straight y squared equals 10 straight x

Solution

straight y squared equals 10 straight x
It is the equation of parabola in the standard form straight y squared equals 4 ax comma space straight a greater than 0 and open towards the right.
Comparing with straight y squared space equals space 4 ax comma we have 4a = 10 rightwards double arrow space space straight a equals 5 over 2

∴  The co-ordinates of the focus S are (a, 0) left right arrow open parentheses 5 over 2 comma space 0 close parentheses
     The equation of the axis of the parabola is y = 0 (x - axis).
     The equation of directrix is x + a = 0 or space space straight x plus 5 over 2 equals 0 space or space 2 straight x plus 5 equals 0
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