Expression 12: StartFraction, left parenthesis, "x" plus 3.1 , right parenthesis squared Over StartNestedFraction, 18 NestedOver 25 , EndNestedFraction , EndFraction plus left parenthesis, "y" plus 5 , right parenthesis squared less than or equal to left parenthesis, 3 halves , right parenthesis squaredx+3.121825+y+52≤322
12
Expression 13: left parenthesis, StartFraction, "x" plus 3.1 Over StartRoot, StartNestedFraction, 18 NestedOver 25 , EndNestedFraction , EndRoot times 3 halves , EndFraction , right parenthesis squared plus left parenthesis, StartFraction, "y" plus 5 Over 3 halves , EndFraction , right parenthesis squared less than or equal to 1x+3.11825·322+y+5322≤1
13
Expression 14: left parenthesis, StartFraction, "x" plus 3.1 Over StartNestedFraction, 9 StartRoot, 2 , EndRoot NestedOver 10 , EndNestedFraction , EndFraction , right parenthesis squared plus left parenthesis, StartFraction, "y" plus 5 Over 3 halves , EndFraction , right parenthesis squared less than or equal to 1x+3.192102+y+5322≤1
14
Create horizontal line whose fill covers the top half of the ellipse.
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Expression 16: "y" greater than or equal to negative 5y≥−5
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Now get intersection using this trick:
1. Convert both into <= 0 form
2. Take their maximum.
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Expression 18: left parenthesis, StartFraction, "x" plus 3.1 Over StartNestedFraction, 9 StartRoot, 2 , EndRoot NestedOver 10 , EndNestedFraction , EndFraction , right parenthesis squared plus left parenthesis, StartFraction, "y" plus 5 Over 3 halves , EndFraction , right parenthesis squared minus 1 less than or equal to 0x+3.192102+y+5322−1≤0
18
Expression 19: negative "y" minus 5 less than or equal to 0−y−5≤0
19
Expression 20: max left parenthesis, left parenthesis, StartFraction, "x" plus 3.1 Over StartNestedFraction, 9 StartRoot, 2 , EndRoot NestedOver 10 , EndNestedFraction , EndFraction , right parenthesis squared plus left parenthesis, StartFraction, "y" plus 5 Over 3 halves , EndFraction , right parenthesis squared minus 1 , negative "y" minus 5 , right parenthesis less than or equal to 0maxx+3.192102+y+5322−1,−y−5≤0
20
Add rotation back in, either using "with" or just manually doing it by hand.
21
Expression 22: left parenthesis, max left parenthesis, left parenthesis, StartFraction, "x" plus 3.1 Over StartNestedFraction, 9 StartRoot, 2 , EndRoot NestedOver 10 , EndNestedFraction , EndFraction , right parenthesis squared plus left parenthesis, StartFraction, "y" plus 5 Over 3 halves , EndFraction , right parenthesis squared minus 1 , negative "y" minus 5 , right parenthesis with "x" equals "x" cos left parenthesis, negative "z" Subscript, 2 , Baseline , right parenthesis plus "y" sin left parenthesis, negative "z" Subscript, 2 , Baseline , right parenthesis , "y" equals "y" cos left parenthesis, negative "z" Subscript, 2 , Baseline , right parenthesis minus "x" sin left parenthesis, negative "z" Subscript, 2 , Baseline , right parenthesis , right parenthesis less than or equal to 0 Has graph.maxx+3.192102+y+5322−1,−y−5withx=xcos−z2+ysin−z2,y=ycos−z2−xsin−z2≤0
22
Expression 23: left parenthesis, max left parenthesis, left parenthesis, StartFraction, "x" cos left parenthesis, negative "z" Subscript, 2 , Baseline , right parenthesis plus "y" sin left parenthesis, negative "z" Subscript, 2 , Baseline , right parenthesis plus 3.1 Over StartNestedFraction, 9 StartRoot, 2 , EndRoot NestedOver 10 , EndNestedFraction , EndFraction , right parenthesis squared plus left parenthesis, StartFraction, "y" cos left parenthesis, negative "z" Subscript, 2 , Baseline , right parenthesis minus "x" sin left parenthesis, negative "z" Subscript, 2 , Baseline , right parenthesis plus 5 Over 3 halves , EndFraction , right parenthesis squared minus 1 , negative left parenthesis, "y" cos left parenthesis, negative "z" Subscript, 2 , Baseline , right parenthesis minus "x" sin left parenthesis, negative "z" Subscript, 2 , Baseline , right parenthesis , right parenthesis minus 5 , right parenthesis , right parenthesis less than or equal to 0 Has graph.maxxcos−z2+ysin−z2+3.192102+ycos−z2−xsin−z2+5322−1,−ycos−z2−xsin−z2−5≤0