If (x,y) satisfies the simultaneous equations
3xy - 4x^2 - 36y + 48x = 0
x^2 - 2y^2 = 16
where x and y may be complex numbers, determine all possible values of y^2.
+130044 3xy - 4x^2 - 36y + 48x = 0 (1)
x^2 - 2y^2 = 16 (2)
Look at the graph here :
https://www.desmos.com/calculator/kfu7s3izs1
Note that, oddly, the first graph is a straight line ......this is known as a "degenerate conic" which never intersects the second function (a hyperbola)....so....no solutions
