DailyDesmos 141A

Now substitute a=x and h=y

Ausdruck 22: .5 equals "x" left parenthesis, negative 1 minus "y" , right parenthesis squared minus "x" "y" squared

Ausdruck 23: 1 equals "x" left parenthesis, .5 minus "y" , right parenthesis squared minus "x" "y" squared

Interesting, Desmos won't graph those equations. I guess I will have to simplify them myself.

Ausdruck 25: StartFraction, .5 Over "x" , EndFraction equals 1 plus 2 "y"

Ausdruck 26: StartFraction, 1 Over "x" , EndFraction equals .2 5 minus "y"

Clicking on their intersection point, verifies the values I had above.

Finally, we can create a general case where we are given two coordinate points and (0,0)

Ausgeblendete Bezeichnung: left parenthesis, "a" Subscript, 1 , Baseline , "b" Subscript, 1 , Baseline , right parenthesis

Bezeichnung

Ausdruck 30: "a" Subscript, 1 , Baseline equals 0.3 4

negative 10

Ausdruck 31: "b" Subscript, 1 , Baseline equals negative 0.8 3

negative 10

Ausgeblendete Bezeichnung: left parenthesis, "a" Subscript, 2 , Baseline , "b" Subscript, 2 , Baseline , right parenthesis

Bezeichnung

Ausdruck 33: "a" Subscript, 2 , Baseline equals negative 2.0 3

negative 10

Ausdruck 34: "b" Subscript, 2 , Baseline equals 0.4 5

negative 10

Ausdruck 35: StartFraction, "b" Subscript, 1 , Baseline Over "x" , EndFraction equals left parenthesis, "a" Subscript, 1 , Baseline , right parenthesis squared minus 2 "a" Subscript, 1 , Baseline "y"

Ausdruck 36: StartFraction, "b" Subscript, 2 , Baseline Over "x" , EndFraction equals "a" squared minus 2 "a" Subscript, 2 , Baseline "y"

Showing the lines above will have an intersection of (A, h_1) Those values can also be solved algebraically.

Ausdruck 38: "y" equals "A" left parenthesis, "x" minus "h" Subscript, 1 , Baseline , right parenthesis squared minus "A" times "h" squared

Ausdruck 39: "h" Subscript, 1 , Baseline equals StartFraction, "b" Subscript, 2 , Baseline "a" squared minus "b" Subscript, 1 , Baseline left parenthesis, "a" Subscript, 2 , Baseline , right parenthesis squared Over 2 "a" Subscript, 1 , Baseline "b" Subscript, 2 , Baseline minus 2 "a" Subscript, 2 , Baseline "b" Subscript, 1 , Baseline , EndFraction

equals

negative 1.1 3 3 3 5 3 0 2 5 6 5

Ausdruck 40: "A" equals left parenthesis, StartFraction, "b" Subscript, 2 , Baseline Over "a" squared minus 2 "a" Subscript, 2 , Baseline "h" Subscript, 1 , Baseline , EndFraction , right parenthesis

equals

negative 0.9 3 6 4 9 8 5 6 2 7 6

Ausdruck 41: