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

question 114

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) \(\left| \frac { x } { y } \right| \leq \frac { 1 } { 5 }\)

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