### Instruction: Which type of conic section is described by the equation \[|y+5| = \sqrt{(x-2)^2 + y^2}?\]Enter "C" for circle, "P" for parabola, "E" for ellipse, "H" for hyperbola, and "N" for none of the above.### Response: To determine the type of conic section, I need to rewrite the equation in a standard form.
I notice that the right-hand side of the equation is the distance from the point (x,y) to the point (2,0).
This means that the left-hand side, |y+5|, must also be a distance.
In fact, it is the distance from the point (x,y) to the line y = -5.
Therefore, the equation describes the set of points that are equidistant from the point (2,0) and the line y = -5.
This is the definition of a parabola with a focus at (2,0) and a directrix at y = -5.
So the answer is P for parabola.