Answer: p = 4, r = 4
Step-by-step explanation:
The equation of a circle is: (x - h)² + (y - k)² = r² where
- (h, k) is the center of the circle
- r is the radius of the circle
Complete the square:
x² - 10x + _____ + y² + py + _____ = -13 + ___ + ___
x² - 10x + (-10/2)² + y² + py + (p/2)² = -13 + (-10/2)² + (p/2)²
(x - 5)² + (y + p/2)² = -13 + 25 + (p/2)²
↓ ↓ |_____↓_____|
h = 5 k = -p/2 r²
Given: (h, k) = (5, -2)
-2 = -p/2
-4 = -p
4 = p
r² = -13 + 25 + (p/2)²
= -13 + 25 + (4/2)²
= -13 + 25 + 4
= 16
[tex]\sqrt{r^2}=\sqrt{16}[/tex]
r = 4
