Certainly! Let's work through the given equation to determine the value that replaces the "?".
The equation we have is:
[tex]\[ (x - 2)^2 + (y - [?])^2 = \text{constant} \][/tex]
This is the general form of the equation of a circle. A circle's equation in standard form is:
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
where:
- [tex]\( (h, k) \)[/tex] is the center of the circle.
- [tex]\( r \)[/tex] is the radius of the circle.
Looking at the provided equation:
[tex]\[ (x - 2)^2 + (y - [?])^2 \][/tex]
We can see that the circle is centered at [tex]\( (h, k) \)[/tex]. In this case, [tex]\( h = 2 \)[/tex] and [tex]\( k \)[/tex] is represented by "[?]".
Thus, to replace "[?]" with the correct term, we see that [tex]\( k \)[/tex] itself is unknown and should remain as it is until further context is provided. This means that the expression inside the parentheses for [tex]\( y \)[/tex] is:
[tex]\[ (y - k) \][/tex]
Therefore, the term that replaces "[?]" is simply:
[tex]\[ y - k \][/tex]
So the full equation is:
[tex]\[ (x - 2)^2 + (y - k)^2 \][/tex]
In conclusion, the value replacing "[?]" in the equation is:
[tex]\[ y - k \][/tex]
