Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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]


We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.