Answer:
The answer to your question is: 10 units
Step-by-step explanation:
P (-3, -12)
1.- Find the center of the circle
x² + y² = 6x - 8y + 24
x² - 6x + ( )² + y² + 8y + ( )² = 24
x² - 6x + (3)² + y² + 8y + (4)² = 24 + 9 + 16
(x - 3)² + (y + 4)² = 49
Center (3, -4)
2.- Find the distance between the center and the point given
Formula
d = [tex]\sqrt{(x2- x1)^{2} + (y2 - y1)^{2} }[/tex]
Substitution
d = [tex]\sqrt{(-3 - 3)^{2} + (-12 +4)^{2} }[/tex]
d = [tex]\sqrt{(-6)^{2} + (-8)^{2} }[/tex]
d = [tex]\sqrt{36 + 64} }[/tex]
d = [tex]\sqrt{100}[/tex]
d = 10 units
