Find the equation of the circle that passes through the origin and has its center at (-3,4).

\( equation\ of\ the\ circle:(x-a)^2+(y-b)^2=r^2\\\\(a;\ b)\ is\ a\ cener\ of\ the\ circle\\\\(a;\ b)=(-3;-4)\\\\r-radius\ of\ the\ circle\\\\r=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\Answer:(x+3)^2+(y+4)^2=5^2\to(x+3)^2+(y+4)^2=25 \)

If the center is at (-3,4) and the origin is on the circle, then the radius

of the circle is the distance between the origin and (-3,4).

R² = (-3)² + (-4)²

R² = 9 + 16

R² = 25

R = 5

The equation of the circle is [ (x + 3)² + (y + 4)² = 25 ].

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