To write $(x+4)^2 + (y+3)^2 = 25$ in general form, expand the equation and rearrange terms into the form $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$. Here are the steps:

1. Expand the terms:

$(x+4)^2 = x^2 + 8x + 16$ $(y+3)^2 = y^2 + 6y + 9$

Substitute these expansions into the equation: $x^2 + 8x + 16 + y^2 + 6y + 9 = 25$

2. Combine like terms:

$x^2 + y^2 + 8x + 6y + 16 + 9 - 25 = 0$ $x^2 + y^2 + 8x + 6y + 0 = 0$

Final General Form:

$x^2 + y^2 + 8x + 6y = 0$

Would you like a step-by-step explanation of any part of this process?

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5 Related Questions:

1. How do you find the center and radius of a circle given its general equation?
2. How do you convert a general form equation of a circle back into standard form?
3. What is the geometric significance of each term in the circle equation?
4. How can you derive the equation of a circle from three given points?
5. How do you identify if an equation represents a circle, ellipse, or other conic section?

Tip:

Always double-check your expansions and combine like terms carefully to avoid errors when converting equations!