Find maximum value of $\frac xy$

Using the (7,24,25) Pythagorean triangle in the diagram, I get the tangent point $$ \left( \frac{96}{5}, \frac{72}{5} \right) $$ and the maximum of $x/y$ on the circle as $4/3.$

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$x=15+7\cos2t,y=20+7\sin2t$

Use Weierstrass Substitution (https://proofwiki.org/wiki/Weierstrass_Substitution)

and Minimum value of given expression