Răspuns:
a)
[tex]pasi \: pentru \: formla \: patratica[/tex]
[tex]x { }^{2} + 4x + y {}^{2} - 6y + 13 = 0[/tex]
[tex]x = \frac{ - 4 + \sqrt{4 {}^{2} - 4(y {}^{2} - 6y + 13)} }{2} \\ [/tex]
[tex]x = \frac{ - 4 + \sqrt{16} - 4y + 24y - 52}{2}[/tex]
[tex]x = \frac{ - 4 + \sqrt{ - 4(y - 3) {}^{2} } }{\\ 2} [/tex]
[tex]x = \sqrt{ - (y - 3) {}^{2} - 2 } \\ x = - \sqrt{ - (y - 3) {}^{2} - 2} [/tex]
asta a fost pentru x
[tex]y {}^{2} - 6y + x { }^{2} + 4x + 13 = 0[/tex]
[tex]y = \frac{ - ( - 6) + \sqrt{( - 6) {}^{2} - 4(x {}^{2} } + 4 {}^{2} + 13)}{ 2} [/tex]
[tex]y = \frac{ - ( - 6) + \sqrt{36 - 4x {}^{2} - 16x} - 52} {2} [/tex]
[tex]y = \frac{2 \sqrt{ - (x + 2) {}^{2} } + 6 }{ \\ 2} [/tex]
[tex]y = \sqrt{ - (x + 2) {}^{2} + 3 } \\ y = - \sqrt{ - (x + 2) {}^{2} + 3 } [/tex]
