Solve the Problem $f ( x , y ) = \sum _ { n = 0 } ^ { \infty } \left( \frac { x } { y } \right) ^ { n }$

Multiple Choice

Solve the problem.
-Find an equation for the level curve of the function $f ( x , y ) = \sum _ { n = 0 } ^ { \infty } \left( \frac { x } { y } \right) ^ { n }$ that passes through the point $( 1,5 )$ .

A) $\left| \frac { x } { y } \right| = \frac { 1 } { 5 }$
B) $x = 5 y$
C) $\left| \frac { x } { y } \right| = 5$
D) $\left| \frac { x } { y } \right| \leq \frac { 1 } { 5 }$