GEOmETRIA 149 INVALSI 2019 Considera l ellisse rappresentata in figura. [ ] y 3 2 1 O 1 2 3 4 x Indica se ciascuna delle seguenti affermazioni è vera (V) o falsa (F). V F 1. La retta di equazione y = x 1 è esterna all ellisse. V F 2. La retta di equazione y = 2 è secante l ellisse. V F 3. La retta di equazione y = x è tangente all ellisse. V F 4. La retta di equazione y = 1 x è esterna all ellisse. PRACTICE WITH CLIL Second-order symmetric systems 1. In a second-order system of this type: x+y=s {xy = p with s, p R by changing x with y and viceversa we obtain the system: y+x=s {yx = p which, no doubt, is in all similar to the preceding one. A system like this is called symmetric. Its name is justified by the fact that in the Cartesian plane, «change x with y means to pass from a point A(xA ; yA) to its correspondent A (yA ; xA ) in the symmetry with respect to the bisector of the first and of the third quadrant of the Cartesian plane. In the symmetric system considered above, spot the intersections between a straight line perpendicular to the bisector, and an equilateral hyperbola. y A A O 496 x