In each of the, find the equation of the parabola that satisfies the given conditions:

Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis.


Since, the vertex is (0, 0) and the parabola is symmetric about the y-axis, the equation of the parabola is either of the from x2=4ay or x2 = -4ay.


The parabola passes through point (5, 2), which lies in the first quadrant.


Thus, the equation of the parabola is of the form x2 = 4ay, while point (5, 2) must satisfy the equation x2 = 4ay.


Thus,


52 = 4a(2)


25 = 8a


a = 25/8


Thus, the equation of the parabola is




2x2 = 25y


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