Answer:
Step-by-step explanation:
I am not exactly sure why it is undefined, but in my thought process below, I have noticed a trend, and it might help spark some thoughts.
(y-5)² + (x+5)² = r²
r = 4.1
x = -9.1
y = ?
If we try plugging in the known values to solve for y, then...
(y-5)² + (-9.1+5)² = 4.1²
(y-5)² + 16.81 = 16.81
(y-5)² = 0
y-5 = √0
y = 5
Now solving the equation does show that y exists, so maybe it's a domain/range problem. So let's find the domain and range.
The standard form is (x-a)² + (y-b)² = r², so since we have (y-5)² + (x+5)² = r², our (a is -5) and (b is 5) (and r is 4.1)
The domain of a circle is a-r ≤ x ≤ a+r, which gives (-5)-4.1 ≤ x ≤ (-5)+4.1
So our domain is -9.1 ≤ x ≤ -0.9
The range of a circle is b-r ≤ y ≤ b+r, which gives (5)-4.1 ≤ y ≤ (5)+4.1
So our range is 0.9 ≤ y ≤ 9.1
When x = -9.1, it is within the domain.
When y = 5, it is also within the domain.
Which means that the y value should exists.
BUT...
Here's a trend that I have noticed on desmos...
When (y-5)² + (x+5)² = r² and r = 4.1, y is undefined at the domain boundaries of -9.1 and -0.9
When (y-5)² + (x+5)² = r² and r = - 4.1, y is undefined at the domain boundaries of -9.1 and -0.9
When (y-5)² + (x+4)² = r² and r = 4.1, y is undefined at the domain boundaries of -8.1 and -0.1
When (y-4)² + (x+5)² = r² and r = 4.1, y is undefined at the domain boundaries of -9.1 and -0.9
When (y-5)² + (x+6)² = r² and r = 4.1, y is undefined at the domain boundaries of -10.1 and -1.9
When (y-6)² + (x+5)² = r² and r = 4.1, y is defined (y=6) at the domain boundaries of -9.1 and -0.9
When (y-6)² + (x+6)² = r² and r = 4.1, y is defined (y=6) at the domain boundaries of -10.1 and -1.9
When (y-6)² + (x+5)² = r² and r = 8.3, y is undefined at the domain boundaries of -13.3 and 3.3
When (y-6)² + (x+6)² = r² and r = 8.3, y is undefined at the domain boundaries of -14.3 and 2.3
I do not understand the trend despite of spending last night and today thinking about it. But Hope it helps. (If you saw me answering yesterday night, yea that's me, I ended up deleting it cuz I can't think it through, but then I thought that maybe it could help spark your thoughts, so here it is)
