Respuesta :

carlosego

By definition, the equation of a circle, centered at point (a, b) is


[tex](x-a) ^ 2 + (y-b) ^ 2 = r ^ 2[/tex]


Where r is the radius of the circumference, and is calculated as the distance from the center to any point belonging to the circumference.



We have the center (5, -4) and the point through which the circumference passes (-3, 2), then:

[tex]a = 5\\b = -4\\r = \sqrt {(- 3-5) ^ 2 + (2 + 4) ^ 2}\\r = 10[/tex]


Finally, the equation of the circumference is:

[tex](x-5) ^ 2 + (y + 4) ^ 2 = 10 ^ 2[/tex]

alinakincsem

Answer:

[tex](x-5)^2+(y+4)^2 = 10^2[/tex]

Step-by-step explanation:

The formula for the equation of a circle centered at the origin (0, 0) is [tex]x^2+y^2 = r^2[/tex] but when the center of the circle is not the origin, then you move it back to the center mathematically.

So we have:

[tex](x-5)^2+(y+4)^2 = r^2[/tex]

Finding the radius [tex]r[/tex] by calculating the distance from the center to the given point:

[tex]r= \sqrt{(5-(-3))^2+(-4-2)^2} = \sqrt{64+36} = \sqrt{100} = 10[/tex]

Therefore, the equation of this circle will be:

[tex](x-5)^2+(y+4)^2 = 10^2[/tex]


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