At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
[tex]The\ standard\ form\ of\ the\ circle:\\\\(x-a)^2+(y-b)^2=r^2\\\\where\\(a;\ b)\ are\ the\ coordinates\ of\ a\ center\ of\ the\ circle\\r\ is\ a\ radius\ of\ the\ circle\\------------------------[/tex]
[tex]2x^2+2y^2-20x-8y+50=0\ \ \ \ |divide\ both\ sides\ by\ 2\\\\x^2+y^2-10x-4y+25=0\\\\x^2-10x+y^2-4y=-25\\\\x^2-2x\cdot5+y^2-2y\cdot2=-25\\\\\underbrace{x^2-2x\cdot5+5^2}_{(*)}-5^2+\underbrace{y^2-2y\cdot2+2^2}_{(*)}-2^2=-25\\(x-5)^2-25+(y-2)^2-4=-25\\\\(x-5)^2+(y-2)^2-29=-25\\\\(x-5)^2+(y-2)^2=-25+29[/tex]
[tex]\boxed{(x-5)^2+(y-2)^2=4}\\\\the\ center:(5;\ 2)\\the\ radius:r=\sqrt4=2[/tex]
[tex](*)\ (a-b)^2=a^2-2ab+b^2[/tex]
[tex]2x^2+2y^2-20x-8y+50=0\ \ \ \ |divide\ both\ sides\ by\ 2\\\\x^2+y^2-10x-4y+25=0\\\\x^2-10x+y^2-4y=-25\\\\x^2-2x\cdot5+y^2-2y\cdot2=-25\\\\\underbrace{x^2-2x\cdot5+5^2}_{(*)}-5^2+\underbrace{y^2-2y\cdot2+2^2}_{(*)}-2^2=-25\\(x-5)^2-25+(y-2)^2-4=-25\\\\(x-5)^2+(y-2)^2-29=-25\\\\(x-5)^2+(y-2)^2=-25+29[/tex]
[tex]\boxed{(x-5)^2+(y-2)^2=4}\\\\the\ center:(5;\ 2)\\the\ radius:r=\sqrt4=2[/tex]
[tex](*)\ (a-b)^2=a^2-2ab+b^2[/tex]
[tex]"Standard Form" \ for \ the \ equation \ of \ a \ circle : \\\\(x-a)^2+(y-b)^2=r^2 \\ the \ center \ (a,b)\\radius \ r \\\\ 2x^2 + 2y^2 -20x - 8y + 50 = 0 \ \ \ Divide \ thru \ by \ 2 \\\\x^2 + y^2 -10x - 4y + 25 = 0[/tex]
[tex]x^2-10x +25 +y^2-4y +4-4 =0 \\\\(x^2-10x +25) +(y^2-4y +4)=4 \\\\(x-5)^2+(y-2)^2=2^2[/tex]
[tex]x^2-10x +25 +y^2-4y +4-4 =0 \\\\(x^2-10x +25) +(y^2-4y +4)=4 \\\\(x-5)^2+(y-2)^2=2^2[/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
