What is the distance between the center of the circle with equation $x^2+y^2=6x-8y+24$ and the point $(-3,-12)$?
1 answer:
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} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28x2-%20x1%29%5E%7B2%7D%20%2B%20%28y2%20-%20y1%29%5E%7B2%7D%20%7D)
Substitution
d = ![\sqrt{(-3 - 3)^{2} + (-12 +4)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28-3%20-%203%29%5E%7B2%7D%20%2B%20%28-12%20%2B4%29%5E%7B2%7D%20%7D)
d = ![\sqrt{(-6)^{2} + (-8)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28-6%29%5E%7B2%7D%20%2B%20%28-8%29%5E%7B2%7D%20%7D)
d = ![\sqrt{36 + 64} }](https://tex.z-dn.net/?f=%5Csqrt%7B36%20%2B%2064%7D%20%7D)
d = ![\sqrt{100}](https://tex.z-dn.net/?f=%5Csqrt%7B100%7D)
d = 10 units
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