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in Parabola by (44.7k points)
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Find the equation of the parabola, which is symmetric about the y-axis and passes through the point P(2, -3).

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The equation of a parabola with vertex at the origin and symmetric about the y-axis is x2 = 4ay 

Since point P(2,-3) passes through above parabola we can write, 

22 = 4a(-3)

4 = -12a

a = \(-\frac{1}{3}\) 

Therefore, the equation of a parabola is

x2 = 4.\(\Big(-\frac{1}{3}\Big)y\) 

x2 = \(-\frac{4}{3}y\) 

3x2 = -4y

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