Write as a Vector Equality y^2=(x^2-9) , (x-3)^2+(y+3)^2=9

Problem

y2=x2−9,(x−3)2+(y+3)2=9

Solution

1. Identify the given equations as a system representing the intersection of a hyperbola and a circle in the x*yplane.

2. Define the vector r as the position vector of a point (x,y) that satisfies both equations simultaneously.

3. Express the system using vector notation by setting the vector r equal to the set of coordinates that satisfy the constraints.

4. Formulate the vector equality by representing the variables as components of a vector v=<x,y> such that the equations hold true.

Final Answer

<y2,(x−3)2+(y+3)2>=<x2−9,9>

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