Answer:
(a) (x+9)²+(y-5)²=56
(b) 7.4833
Step-by-step explanation:
The standard form for the equation of a circle is (x-h)²+(y-k)²=r².
Expanded a bit, this is x²-2hx+h²+y²-2ky+k²=r².
Rearrange this to resemble our equation: x²+y²+(-2h)x+(-2k)y=(r²-h²-k²)
Looking at our equation, x²+y²+18x-10y=-50, we can say-2h=18, -2k=-10, and r²-h²-k²=-50.
-2h=18
h=-9
-2k=-10
k=5
r²-h²-k²=-50
r²-(-9)²-(5²)=-50
r²-81-25=-50
r²=106-50
r²=56
So since we know h, k, and r², we can say x²+y²+18x-10y=-50 =
(x+9)²+(y-5)²=56
(b)
For an equation in standard from, r is the radius.
In part a, we found r²=56.
r=[tex]\sqrt{56}[/tex]=7.4833
