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3 years ago

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

Mathematics

1 answer:

kvasek [131]3 years ago

3 0

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

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jarptica [38.1K]

We are given

△ABC, m∠A=60° m∠C=45°, AB=8

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we can plug values

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