The equation for a circle is as followed:

where the center of the circle is at (h,k) and the radius of the circle is r.
We are given (h,k) and need to find the radius. To do so, we can use the distance formula to find the distance from the center to the point on the circle:

Plug in the two points:



If the distance from the center to the edge of the circle is the square root of 117, then r^2 = 117.
The answer is:
Multiply you first equation by 2 to get 4x + 10y = 22
Now the x terms can be eliminated and cancelled out using elimination.
4x + 10y = 22
4x + 3y = 1
To eliminate you need to "subtract", so you need to multiply one of the equations by -1.
4x + 10y = 22
-4x -3y = -1
------------------
0 + 7y = 21
y = 3
Now plug 3 into either one of the equations to get x.
The area of the rectangle is 84 inches :)
It has no solution bc there or no point and because its not the same line
This area is equal to the sum of a circle with a radius of 5/2 in and a rectangle 5 by 15 in so:
A=πr^2+xy
A=π(2.5)^2+5*15
A=6.25π+75 in^2
A≈94.63 in^2 (to nearest hundredth) so
A≈95 in^2 (to nearest whole square inch)