Answer: \((x-5)^2+(y+4)^2=100\)
Step-by-step explanation:
We know that the general equation of a circle can be written as :
\((x-h)^2+(y-k)^2=r^2\) (1), where (center )= (h,k) and r= radius
As per given , we have
(h,k) = (5,-4)
(x,y) =(-3,2)
Substitute these value in equation (1), we get
\((-3-5)^2+(2-(-4))^2=r^2\\\\\Rightarrow\ (-8)^2+(2+4)^2=r^2\\\\\Rightarrow\ 64+6^2=r^2\\\\\Rightarrow\ 64+36=r^2\\\\\Rightarrow\ 100=r^2\\\\\Rightarrow\ r=\sqrt{100}=\pm10\)
Since radius cannot be negative , thus r= 10 units
Put value of \(r^2\) and (h,k) in equation (1), we get
\((x-5)^2+(y+4)^2=100\)
Thus , the equation of given circle is \((x-5)^2+(y+4)^2=100\).
