Binomial Theorem

Question
CBSEENMA11015130

Find the co-ordinates of a point on the parabola y2 = l8x, where the ordinate is 3 times the abscissa.

Solution

Let the point be straight P space left parenthesis straight alpha comma space straight beta right parenthesis
∴     straight beta equals 3 straight alpha                                                                          [∵   Ordinate is 3 times the abscissa]
space space space space space straight P left parenthesis straight alpha comma space straight beta right parenthesis lies on the parabola
rightwards double arrow               straight beta squared equals 18 straight alpha space space rightwards double arrow space space left parenthesis 3 straight alpha right parenthesis squared space equals space 18 straight alpha space space space rightwards double arrow space space straight a squared space equals space 2 straight alpha
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#6 {main}</pre>
When space space space straight alpha equals 0 comma space straight beta equals 0 space and space when space straight alpha equals 2 comma space straight beta equals 6
Hence, the coordinates of the point are (2, 6).

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