Find the equation of the parabola with vertex at (0,0) and focus at (0,2).
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Step-by-Step Solution
Step 1: Identify the orientation of the parabola
The vertex of the parabola is at the origin (0,0) and the focus is at (0,2). Since the x -coordinate of the vertex and focus are the same, and the y -coordinate of the focus is greater than the y -coordinate of the vertex, the parabola opens upwards.
Step 2: Determine the value of 'a'
For a parabola with vertex at (0,0) and focus at (0,a), the distance from the vertex to the focus is a. In this case, a is the absolute difference between the y -coordinates of the focus and the vertex, which is 2.
Step 3: Write the standard equation of the parabola
Since the parabola opens upwards and its vertex is at the origin, its standard equation is of the form x2=4ay.
Step 4: Substitute the value of 'a' into the equation
Now, substitute the value of a=2 into the standard equation x2=4ay to find the specific equation for this parabola.
Step 5: Simplify the equation
Perform the multiplication to simplify the equation and obtain the final equation of the parabola.