Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

The center of a cricle ids (h,7) and the radius is 10. The circle passes through (3,-1). Find all possible values of h.

Sagot :

[tex]center\ of\ a\ circle:(a;\ b)\\\\radius:r\\\\(x-a)^2+(y-b)^2=r^2\\\\========================\\\\(h;\ 7);\ r=10\\\\(x-h)^2+(y-7)^2=10^2\\\\========================[/tex]

[tex]The\ circle\ passes\ throught\ (3;-1).\\\\Substitute\ x=3\ and\ y=-1:\\\\(3-h)^2+(-1-7)^2=100\\\\(3-h)^2+(-8)^2=100\\\\(3-h)^2+64=100\ \ \ /-64\\\\(3-h)^2=36\iff3-h=\pm\sqrt{36}\\\\3-h=-6\ or\ 3-h=6\\-h=-6-3\ or\ -h=6-3\\-h=-9\ or\ -h=3\\h=9\ or\ h=-3\\\\Answer:h=9\ or\ h=-3[/tex]
kate200468
[tex]equation\ of\ a\ circle:\\\\(x-h)^2+(y-7)^2=10^2\\\\if\ \ (x;y)=(3;-1),\ then\ \ (3-h)^2+(-1-7)^2=100\\\\(3-h)^2+64=100\\\\ (3-h)^2=36\ \ \ \Leftrightarrow\ \ \ (3-h=6\ \ \ or\ \ \ 3-h=-6)\\\\3-h=6\ \ \ \ \ \Rightarrow\ \ \ h=-3\\3-h=-6\ \ \ \Rightarrow\ \ \ h=9\\\\Ans.\ h=-3\ \ or\ \ h=9[/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.