Can someone help me finding maximum value of a ratio in quadratic function in 2 variables using proper mathematical methods.?
Question is as below.
If x and y are real numbers such that $x^2 -10x+y^2 +16=0$, determine the maximum value of the ratio $y/x$
I know there is Ramban method to solve this. Taking $y/x=k --> y=kx$ and forming equation in x , then applying $^2 - 4ac >=0$ for max min value of k.
Is there any way to using differentiation ?
Sorry in advance if this is a repeat. I am new to platform.