Answer:
n = - 4, n = 10
Step-by-step explanation:
Since the point (6, n) lies on the circle then the coordinates of the point make the equation true.
Substitute x = 6 and y = n into the equation
(6 - 1)² + (n - 3)² = 74, that is, expanding using FOIL
5² + n² - 6n + 9 = 74 ← simplifying
34 + n² - 6n = 74 ( subtract 74 from both sides and rearrange )
n² - 6n - 40 = 0 ← in standard form
(n - 10)(n + 4) = 0 ← in factored form
Equate each factor to zero and solve for n
n - 10 = 0 ⇒ n = 10
n + 4 = 0 ⇒ n = - 4
The values of n are - 4 and 10
