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

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) (Show Source): You can put this solution on YOUR website!
A circle is in the form where the center is (h,k) with radius 'r'

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

Plug these values into the equation above to get

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 and .
Also,

is the second point

. So this means that and .

Start with the distance formula.

Plug in , , , and .

Subtract from to get .

Subtract from to get .

Square to get .

Square to get .

Add to to get .

Since the distance is units, the radius is . Square this value to get . So

So the equation of the circle is

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

Also, feel free to check out my tutoring website

Jim
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