The point (6, n) lies on the circle whose equation is (x − 1)2 + (y − 3)2 = 74. Find the values of n.
The values of n are .

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