SOLUTION: the point center at (3,4), graph contains the point (7,9). find the equation of a circle satisfying these conditions given.

Algebra ->  Linear-equations -> SOLUTION: the point center at (3,4), graph contains the point (7,9). find the equation of a circle satisfying these conditions given.      Log On


   

Question 394404: the point center at (3,4), graph contains the point (7,9).
find the equation of a circle satisfying these conditions given.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A circle is in the form %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 where the center is (h,k) with radius 'r'


Since we know that the center is (3,4), we're given that h=3 and k=4


Plug these values into the equation above to get %28x-3%29%5E2%2B%28y-4%29%5E2=r%5E2


So all we really need is the radius 'r'. We can find this by finding the distance from the center (3,4) to the point (7,9) (since this point lies on the circle)


Let's use the distance formula to find this distance


Note: is the first point . So this means that x%5B1%5D=3 and y%5B1%5D=4.
Also, is the second point . So this means that x%5B2%5D=7 and y%5B2%5D=9.


d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%283-7%29%5E2%2B%284-9%29%5E2%29 Plug in x%5B1%5D=3, x%5B2%5D=7, y%5B1%5D=4, and y%5B2%5D=9.


d=sqrt%28%28-4%29%5E2%2B%284-9%29%5E2%29 Subtract 7 from 3 to get -4.


d=sqrt%28%28-4%29%5E2%2B%28-5%29%5E2%29 Subtract 9 from 4 to get -5.


d=sqrt%2816%2B%28-5%29%5E2%29 Square -4 to get 16.


d=sqrt%2816%2B25%29 Square -5 to get 25.


d=sqrt%2841%29 Add 16 to 25 to get 41.


Since the distance is sqrt%2841%29 units, the radius is r=sqrt%2841%29. Square this value to get r%5E2=%28sqrt%2841%29%29=41. So r%5E2=41


So the equation of the circle is %28x-3%29%5E2%2B%28y-4%29%5E2=41


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim