Answer:
B). x^2 + y^2 - 32 = 0
Step-by-step explanation:
If it is tangent to x+y = 8, then the distance from (h,k) to a point on that line can be found by using
d = |A*h+B*k+C| / sqrt(A^2+B^2)
Where Ax + By +c = 0 is the equation of the line and (h,k) is the center of the circle
1x+1y -8 =0
so A =1 B = 1 C = -8
h,k = 0,0
d = |1*0+1*0+-8| / sqrt(1^2+1^2)
d = |-8| / sqrt(2)
d = 8 /sqrt(2)
Multiplying by the sqrt(2)/ sqrt(2) =
d = 8 /sqrt(2) * sqrt(2)/ sqrt(2)
d = 8 sqrt(2)/2
d =4 sqrt(2)
This is the radius
The standard equation for a circle is in vertex form
(x-h) ^2 + (y-k) ^2 = r^2
(x-0)^2 + (y-k) ^2 = (4 sqrt(2))^2
x^2 + y^2 = 16*2
x^2 + y^2 = 32
Rewriting in standard form
x^2 + y^2 -32 = 32-32
x^2 +y^2 -32 =0
