Answered

Join IDNLearn.com today and start getting the answers you've been searching for. Get comprehensive answers to all your questions from our network of experienced experts.

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]
Kate200468idn
[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 value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.