12. 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.
Given a parabola,
with Vertex (0,0), passing through (5,2) and symmetric with respect to the y-axis.
Since the parabola is symmetric with respect to Y=axis, it's axis will ve Y-axis. and since it passes through the point (5,2), it must go through the first quadrant.
So the standard equation of such parabola is
Now since this parabola is passing through (5,2)
Hence the equation of the parabola is