Question

What is the distance between the center of the circle with equation $x^2+y^2=6x-8y+24$ and the point $(-3,-12)$?

Answer 1

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 = $\sqrt{(x2- x1)^{2} + (y2 - y1)^{2} }$

Substitution

d = $\sqrt{(-3 - 3)^{2} + (-12 +4)^{2} }$

d = $\sqrt{(-6)^{2} + (-8)^{2} }$

d = $\sqrt{36 + 64} }$

d = $\sqrt{100}$

d = 10 units