Binomial Theorem

Question
CBSEENMA11015125

Find the equation of the parabola that satisfying the following condition:
Vertex at (0,0), symmetrical about y-axis and passing through the point (2, –3)

Solution

The vertex of the parabola is at (0, 0) and it is symmetrical about the y-axis.
∴    The axis of the parabola is y-axis (x = 0)
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#6 {main}</pre>                                                       ...(i)
Since it passes through the points (2, -3)
∴    2 squared space equals space 4 straight a left parenthesis negative 3 right parenthesis space rightwards double arrow space 4 space equals space minus 12 straight a space rightwards double arrow space straight a equals negative 1 third
Hence, from (i), the equation of the parabola is: straight x squared space equals space 4 open parentheses negative 1 third close parentheses straight y space or space 3 straight x squared space equals space minus 4 straight y

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