Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Convert the general form of the circle given into standard form.
2x^2 + 2y^2 - 20x - 8y + 50 = 0

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]
Lilith
[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]


Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.