(x+1)^2+(y+2)^2=9 General Form

Jasonbradley

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Jun 16, 2024

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Converting the Equation (x+1)² + (y+2)² = 9 to General Form

The equation (x+1)² + (y+2)² = 9 is in standard form, which represents a circle with center (-1, -2) and radius 3. To convert it to general form, we need to expand the squares and rearrange the terms.

Here's how:

1. Expand the squares: (x+1)² + (y+2)² = x² + 2x + 1 + y² + 4y + 4 = 9

2. Rearrange the terms: x² + y² + 2x + 4y + 1 + 4 - 9 = 0

3. Simplify the constant term: x² + y² + 2x + 4y - 4 = 0

Therefore, the general form of the equation (x+1)² + (y+2)² = 9 is:

x² + y² + 2x + 4y - 4 = 0

General form is written as:

Ax² + Bxy + Cy² + Dx + Ey + F = 0

where A, B, C, D, E, and F are constants.

Advantages of General Form:

• More compact representation: It combines all the terms into a single equation.
• Easier for certain operations: Some calculations, like finding the equation of a tangent line, are easier using the general form.

While standard form provides a clear understanding of the circle's center and radius, general form offers a more concise and adaptable representation.