Wrong answer or not

[Loki123]

The question is:
Write the equation of the geometric locus of the centers of the circles tangent to the circle (x + 5) ^ 2 + y ^ 2 = 9 And the line x-2 = 0.
I attached my work. Last picture includes my solution along with solution from the book and the key difference why me and the book got different answers. Who is right?

 

[pka]

There is a miss-match between the statement of the question and the drawing(the graph)
In the graph the larger circle has center [imath]C:(5,0)[/imath] and radius [imath]r=3[/imath]
Therefore its equation is [imath](x{\bf\color{red}{-}5})^2+y^2=9[/imath] not [imath](x+5)^2+y^2=9[/imath]
Thus you need to correct the question.

 

[Dr.Peterson]

The question is:
Write the equation of the geometric locus of the centers of the circles tangent to the circle (x + 5) ^ 2 + y ^ 2 = 9 And the line x-2 = 0.
I attached my work. Last picture includes my solution along with solution from the book and the key difference why me and the book got different answers. Who is right?

View attachment 31463
View attachment 31464

The center of the given circle is at (-5,0), not (5,0) as in your drawing.

As a result x<2, which will affect your handling of x-2.