determiner-les-coordonnes-de-X-et-Y-r-1-

Question Number 213060 by a.lgnaoui last updated on 29/Oct/24

determiner les coordonnes de X et Y

r = 1

Commented by a.lgnaoui last updated on 29/Oct/24

Commented by Frix last updated on 29/Oct/24

{\begin{cases} \frac{x^{2}}{16} + \frac{y^{2}}{4} = 1 \\ {(x - 2)}^{2} + {(y - \sqrt{3})}^{2} = 1 \end{cases}

{\begin{cases} x^{2} = 16 - 4 y^{2} \\ x^{2} + y^{2} - 4 x - 2 \sqrt{3} y + 6 = 0 \end{cases}

Inserting and solving for x

x = - \frac{3 y^{2} + 2 \sqrt{3} y - 22}{4}

Inserting and transforming

y^{4} + \frac{4 \sqrt{3}}{3} y^{3} - \frac{56}{9} y^{2} - \frac{88 \sqrt{3}}{9} y + \frac{76}{3} = 0

This has no useable exact solutions .

y \approx 1.36205409 \Rightarrow x \approx 2.92903306

y \approx 1.93380767 \Rightarrow x \approx 1.02056436

X = (\begin{matrix} 1.02 \\ 1.93 \end{matrix}) Y = (\begin{matrix} 2.93 \\ 1.36 \end{matrix})

Commented by a.lgnaoui last updated on 29/Oct/24

exact . thank you