Question 981324
Your description in #2 does not give enough information to find where the drone will intersect the parabola, and also, the drone cannot fly upward in vertical line only, to pass through two points; only could pass through one point.


Otherwise, for #1, You seem to have most or all the equation correctly.
{{{y=ax^2+36}}} and you know {{{a<0}}}.  Vertex is  (0,36).  You can identify a possible integer point ordered pair from the graph.  Maybe,  (4,20).
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{{{ax^2=y-36}}}
{{{a=(y-36)/x^2}}}
{{{a=(20-36)/16}}}
{{{a=-1}}}
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{{{highlight(y=-x^2+36)}}}----------Equation for the rainbow parabola, which is equivalent to what you found.


Maybe if the proper description for #2, something can be found.  ( I ALREADY EXPLAINED THIS.  IF DRONE MOVES VERTICALLY, INTERSECT IN ONLY ONE POINT; NOT TWO.)