Предмет: Математика,
автор: Nekha
Найти радиус (уравнение окружности):
45-12х+х^2-10у+у^2=0
52-12х+х^2-10у+у^2=0
12-12х+х^2-10у+у^2=0
36-12х+х^2-10у+у^2=0
Ответы
Автор ответа:
2
Уравнение окружности вида 
имеет координаты центра (x₀; y₀) и радиус R
![45-12x+x^2-10y+y^2=0
\\\
x^2-2\cdot6\cdot x+6^2-6^2+y^2-2\cdot5\cdot y+5^2-5^2+45=0
\\\
(x^2-2\cdot6\cdot x+6^2)-36+(y^2-2\cdot5\cdot y+5^2)-25+45=0
\\\
(x-6)^2+(y-5)^2-16=0
\\\
(x-6)^2+(y-5)^2=16
\\\
\Rightarrow R= \sqrt{16} =4](https://tex.z-dn.net/?f=45-12x%2Bx%5E2-10y%2By%5E2%3D0%0A%5C%5C%5C%0Ax%5E2-2%5Ccdot6%5Ccdot+x%2B6%5E2-6%5E2%2By%5E2-2%5Ccdot5%5Ccdot+y%2B5%5E2-5%5E2%2B45%3D0%0A%5C%5C%5C%0A%28x%5E2-2%5Ccdot6%5Ccdot+x%2B6%5E2%29-36%2B%28y%5E2-2%5Ccdot5%5Ccdot+y%2B5%5E2%29-25%2B45%3D0%0A%5C%5C%5C%0A%28x-6%29%5E2%2B%28y-5%29%5E2-16%3D0%0A%5C%5C%5C%0A%28x-6%29%5E2%2B%28y-5%29%5E2%3D16%0A%5C%5C%5C%0A%5CRightarrow+R%3D+%5Csqrt%7B16%7D+%3D4 "45-12x+x^2-10y+y^2=0
\\\
x^2-2\cdot6\cdot x+6^2-6^2+y^2-2\cdot5\cdot y+5^2-5^2+45=0
\\\
(x^2-2\cdot6\cdot x+6^2)-36+(y^2-2\cdot5\cdot y+5^2)-25+45=0
\\\
(x-6)^2+(y-5)^2-16=0
\\\
(x-6)^2+(y-5)^2=16
\\\
\Rightarrow R= \sqrt{16} =4")
![52-12x+x^2-10y+y^2=0
\\\
x^2-2\cdot6\cdot x+6^2-6^2+y^2-2\cdot5\cdot y+5^2-5^2+52=0
\\\
(x^2-2\cdot6\cdot x+6^2)-36+(y^2-2\cdot5\cdot y+5^2)-25+52=0
\\\
(x-6)^2+(y-5)^2-9=0
\\\
(x-6)^2+(y-5)^2=9
\\\
\Rightarrow R= \sqrt{9} =3](https://tex.z-dn.net/?f=52-12x%2Bx%5E2-10y%2By%5E2%3D0%0A%5C%5C%5C%0Ax%5E2-2%5Ccdot6%5Ccdot+x%2B6%5E2-6%5E2%2By%5E2-2%5Ccdot5%5Ccdot+y%2B5%5E2-5%5E2%2B52%3D0%0A%5C%5C%5C%0A%28x%5E2-2%5Ccdot6%5Ccdot+x%2B6%5E2%29-36%2B%28y%5E2-2%5Ccdot5%5Ccdot+y%2B5%5E2%29-25%2B52%3D0%0A%5C%5C%5C%0A%28x-6%29%5E2%2B%28y-5%29%5E2-9%3D0%0A%5C%5C%5C%0A%28x-6%29%5E2%2B%28y-5%29%5E2%3D9%0A%5C%5C%5C%0A%5CRightarrow+R%3D+%5Csqrt%7B9%7D+%3D3 "52-12x+x^2-10y+y^2=0
\\\
x^2-2\cdot6\cdot x+6^2-6^2+y^2-2\cdot5\cdot y+5^2-5^2+52=0
\\\
(x^2-2\cdot6\cdot x+6^2)-36+(y^2-2\cdot5\cdot y+5^2)-25+52=0
\\\
(x-6)^2+(y-5)^2-9=0
\\\
(x-6)^2+(y-5)^2=9
\\\
\Rightarrow R= \sqrt{9} =3")
![12-12x+x^2-10y+y^2=0
\\\
x^2-2\cdot6\cdot x+6^2-6^2+y^2-2\cdot5\cdot y+5^2-5^2+12=0
\\\
(x^2-2\cdot6\cdot x+6^2)-36+(y^2-2\cdot5\cdot y+5^2)-25+12=0
\\\
(x-6)^2+(y-5)^2-49=0
\\\
(x-6)^2+(y-5)^2=49
\\\
\Rightarrow R= \sqrt{49} =7](https://tex.z-dn.net/?f=12-12x%2Bx%5E2-10y%2By%5E2%3D0%0A%5C%5C%5C%0Ax%5E2-2%5Ccdot6%5Ccdot+x%2B6%5E2-6%5E2%2By%5E2-2%5Ccdot5%5Ccdot+y%2B5%5E2-5%5E2%2B12%3D0%0A%5C%5C%5C%0A%28x%5E2-2%5Ccdot6%5Ccdot+x%2B6%5E2%29-36%2B%28y%5E2-2%5Ccdot5%5Ccdot+y%2B5%5E2%29-25%2B12%3D0%0A%5C%5C%5C%0A%28x-6%29%5E2%2B%28y-5%29%5E2-49%3D0%0A%5C%5C%5C%0A%28x-6%29%5E2%2B%28y-5%29%5E2%3D49%0A%5C%5C%5C%0A%5CRightarrow+R%3D+%5Csqrt%7B49%7D+%3D7 "12-12x+x^2-10y+y^2=0
\\\
x^2-2\cdot6\cdot x+6^2-6^2+y^2-2\cdot5\cdot y+5^2-5^2+12=0
\\\
(x^2-2\cdot6\cdot x+6^2)-36+(y^2-2\cdot5\cdot y+5^2)-25+12=0
\\\
(x-6)^2+(y-5)^2-49=0
\\\
(x-6)^2+(y-5)^2=49
\\\
\Rightarrow R= \sqrt{49} =7")
![36-12x+x^2-10y+y^2=0
\\\
x^2-2\cdot6\cdot x+6^2-6^2+y^2-2\cdot5\cdot y+5^2-5^2+36=0
\\\
(x^2-2\cdot6\cdot x+6^2)-36+(y^2-2\cdot5\cdot y+5^2)-25+36=0
\\\
(x-6)^2+(y-5)^2-25=0
\\\
(x-6)^2+(y-5)^2=25
\\\
\Rightarrow R= \sqrt{25} =5](https://tex.z-dn.net/?f=36-12x%2Bx%5E2-10y%2By%5E2%3D0%0A%5C%5C%5C%0Ax%5E2-2%5Ccdot6%5Ccdot+x%2B6%5E2-6%5E2%2By%5E2-2%5Ccdot5%5Ccdot+y%2B5%5E2-5%5E2%2B36%3D0%0A%5C%5C%5C%0A%28x%5E2-2%5Ccdot6%5Ccdot+x%2B6%5E2%29-36%2B%28y%5E2-2%5Ccdot5%5Ccdot+y%2B5%5E2%29-25%2B36%3D0%0A%5C%5C%5C%0A%28x-6%29%5E2%2B%28y-5%29%5E2-25%3D0%0A%5C%5C%5C%0A%28x-6%29%5E2%2B%28y-5%29%5E2%3D25%0A%5C%5C%5C%0A%5CRightarrow+R%3D+%5Csqrt%7B25%7D+%3D5 "36-12x+x^2-10y+y^2=0
\\\
x^2-2\cdot6\cdot x+6^2-6^2+y^2-2\cdot5\cdot y+5^2-5^2+36=0
\\\
(x^2-2\cdot6\cdot x+6^2)-36+(y^2-2\cdot5\cdot y+5^2)-25+36=0
\\\
(x-6)^2+(y-5)^2-25=0
\\\
(x-6)^2+(y-5)^2=25
\\\
\Rightarrow R= \sqrt{25} =5")
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