Question

Пожалуйстааа :сссссс

Answer 1

$11.53.\\\\1)\; \; \left \{ {{x^2+y^2-6x+8y=0} \atop {x^2+y^2+2x-12y+1=10}} \right. \; \left \{ {{(x-3)^2+(y+4)^2=25} \atop {(x+1)^2+(y-6)^2=36}} \right. \\\\C_1(3,-4)\; \; ,\; \; C_2(-1,6)\\\\l:\; \frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}\; \; ,\; \; \frac{x-3}{-1-3}=\frac{y+4}{6+4} \; ,\; \; \frac{x-3}{-4}=\frac{y+4}{10}\; \; ,\; \; \boxed {\; \frac{x-3}{2}=\frac{y-4}{-5}\; }$

$2)\; \; 2)\; \; \left \{ {x^2+{y^2-8x+6y=0} \atop {x^2+y^2-10x-6y+33=0}} \right.\; \left \{ {{(x-4)^2+(y+3)^2=25} \atop {(x-5)^2+(y-3)^2=1}} \right. \\\\C_1(4,-3)\; \; ,\; \; C_2(5,3)\\\\l:\; \frac{x-4}{5-4}=\frac{y+3}{3+3}\; \; ,\; \; \boxed {\; \frac{x-4}{1}=\frac{y+3}{6}\; }$

$11.54.\; 1)\; \; \left \{ {{x^2+y^2-10x-10y+30=0} \atop {x^2+y^2=10}} \right.\; \left \{{-10x-10y+40=0} \atop {x^2+y^2=10}} \right. \; \left \{ {{x+y=4} \atop {x^2+y^2=10}} \right. \\\\\left \{ {{y=4-x} \atop {x^2+y^2=10}} \right.\; \left \{ {{y=4-x} \atop {x^2+(4-x)^2=10}} \right.\; \left \{ {{y=4-x} \atop {2x^2-8x+6=0}} \right.\; \left \{ {{y=4-x} \atop {x^2-4x+3=0}} \right. \\\\\left \{ {{y=4-x} \atop {x_1=1\; ,\; x_2=3}} \right. \; \left \{ {{y_1=3\; ,\; y_2=1} \atop {x_1=1\; ,\; x_2=3}} \right.\\\\A(1,3)\; ,\; B(3,1)$

$l:\; \frac{x-1}{3-1}=\frac{y-3}{1-3}\; \; ,\; \; \boxed {\; \frac{x-1}{2}=\frac{y-3}{-2}\; }$

$2)\; \; \left \{ {{x^2+y^2-4x-2y-15=0} \atop {x^2+y^2+6x+18y-55=0}} \right.\; \left \{ {{x^2+y^2=4x+2y+15} \atop {x^2+y^2=-6x-18y+55}} \right.\; \left \{ {{x^2+y^2=4x+2y+15} \atop {4x+2y+15=-6x-18y+55}} \right. \\\\\left \{ {{x^2+y^2=4x+2y+15} \atop {10x+20y=40}} \right.\; \left \{ {{(4-2y)^2+y^2-4(4-2y)-2y-15=0} \atop {x=4-2y}} \right.\; \left \{ {{5y^2-10y-15=0} \atop {x=4-2y}} \right.\\\\\left \{ {{y^2-2y-3=0} \atop {x=4-2y}} \right. \; \left \{ {{y_1=-1\; ,\; y_2=3} \atop {x_1=6\; ,\; x_2=-2}} \right.$

$A(6,-1)\; \; ,\; \; B(-2,3)\\\\l:\; \frac{x-6}{-2-6}=\frac{y+1}{3+1}\; \; ,\; \; \frac{x-6}{-8}=\frac{y+1}{4}\;\; ,\; \; \boxed{\; \frac{x-6}{2}=\frac{y+1}{-1}\; }$