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Find the equation of the parabola with vertex at origin, symmetric with respect to y-axis and passing through `(2, -2)`

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The vertex of the parabola is at origin and it is symmetric with respect to y axis. also, it passes through `(2,-2)`, a point in the fourth quadrant.
Let its equation be `x=4ay`.....(1)
as is passes through `(2,-2)` we get `2=-4axx-2=>a=2`
...
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