Let $P_1 = (x_1, y_1)$. Describe $P = (x,y)$ in $\mathbb{R}^2$ s.t. $||P-P_1|| = 9$ by identifying conic and finding its equation

Question

Let $P_1 = (x_1, y_1)$. Describe the set of all points $P = (x,y) \in \mathbb{R}^2$ such that $||P-P_1|| = 9$ by identifying the type of conic and finding its equation.

I'm sorry, but this question throws me off in many ways, and I have a number of em like it, I don't know where to begin, or what it even means by describing the set of all points $P = (x,y)$, I don't even see how a norm of an arbitrary vector of this kind set to a number can be a type of conic, I think I need help with this type of problem in general all around .... =\

I tried taking the norm of $P-P_1$ yielding

$\sqrt(x^2-2xx1 +x1^2 + y^2-2yy1+y1^2) = 9$

$x^2-2xx_1 +x_1^2 + y^2-2yy_1+y_1^2 = 81$

but I have no idea where to go from here, or how to "describe the set" or find out what conic its talking about...

Answer 1

we have $(x-x_1)^2+(y-y_1)^2=81$ but this is a circle with radius $r=9$ and centre $M(x_1,y_1)$