Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle. x^2+y^2-8x-6y+9=0
Complete the square on "x" and "y" together: (x^2 - 8x + 16) + (y^2 - 6y + 9) + 9 - 16 - 9 = 0 (x - 4)^2 + (y - 3)^2 = 4^2 So, the center is (4, 3). The radius is 4. To get the intercepts, you set each variable to "0", first "x" and then "y". (0 - 4)^2 + (y - 3)^2 = 4^2 -> y = 3 so, (0, 3) (x - 4)^2 + (0 - 3)^2 = 4^2 -> (x - 4)^2 = 7 x - 4 = +- sqrt(7) -> x = 4 +- sqrt(7)
is the end of this x-4=+-^7
That last intercept is : (4 +- sqrt[7], 0) that's 2 points because of the +-
ok
All good now?
Is there anything you want me to go over in more depth? @artishaalston
this whole class lol
: - )
|dw:1357960262541:dw|Here's a drawing that might help.
Here, you can see that the y-axis is touched at only one point but the x-axis has those 2 points for intercepts.
The key here was "completing the square" on x and y both at the same time. From there, it goes less rocky.
Your general form for a circle will be: (x - h)^2 + (y - k)^2 = r^2 where (h, k) will be your center and "r" is your radius.
Regarding your comment about "the whole class" which is good humor, will be helped by just showing up at Openstudy a lot. There are a lot of helpful people here, so no worries.
|dw:1357960868257:dw|If you need a more complete diagram:
This particular problem, answer, and diagram might be helpful for questions about circles for the future.
Anything else about this problem now?
@artishaalston ?
Good luck to you in all of your studies and so long for now. @artishaalston
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