What is the formula of 2d equation?
2 Answers
The general formula for a 2D linear equation (representing a straight line) is:
\[
Ax + By = C
\]
Where:
- \( A \), \( B \), and \( C \) are constants.
- \( x \) and \( y \) are variables representing coordinates in the 2D plane.
Alternatively, the slope-intercept form of the 2D line equation is:
\[
y = mx + c
\]
Where:
- \( m \) is the slope of the line.
- \( c \) is the y-intercept (the point where the line crosses the y-axis).
\[
Ax + By = C
\]
Where:
- \( A \), \( B \), and \( C \) are constants.
- \( x \) and \( y \) are variables representing coordinates in the 2D plane.
Alternatively, the slope-intercept form of the 2D line equation is:
\[
y = mx + c
\]
Where:
- \( m \) is the slope of the line.
- \( c \) is the y-intercept (the point where the line crosses the y-axis).
The formula for a 2D equation depends on the type of equation you're referring to. Here are some common types of 2D equations and their formulas:
1. **Linear Equation**:
The general form of a linear equation in two dimensions is:
\[
ax + by + c = 0
\]
where \(a\), \(b\), and \(c\) are constants. This represents a straight line in the \(xy\)-plane.
2. **Quadratic Equation**:
The general form of a quadratic equation in two dimensions is:
\[
ax^2 + bxy + cy^2 + dx + ey + f = 0
\]
This represents a conic section (ellipse, parabola, or hyperbola) in the \(xy\)-plane.
3. **Circle**:
The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
4. **Ellipse**:
The standard form of the equation of an ellipse with center \((h, k)\), semi-major axis \(a\), and semi-minor axis \(b\) is:
\[
\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1
\]
5. **Hyperbola**:
The standard form of the equation of a hyperbola with center \((h, k)\), and semi-major axis \(a\) and semi-minor axis \(b\) is:
\[
\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1
\]
or
\[
\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1
\]
Each of these formulas represents different types of curves or shapes in a 2D coordinate system.
1. **Linear Equation**:
The general form of a linear equation in two dimensions is:
\[
ax + by + c = 0
\]
where \(a\), \(b\), and \(c\) are constants. This represents a straight line in the \(xy\)-plane.
2. **Quadratic Equation**:
The general form of a quadratic equation in two dimensions is:
\[
ax^2 + bxy + cy^2 + dx + ey + f = 0
\]
This represents a conic section (ellipse, parabola, or hyperbola) in the \(xy\)-plane.
3. **Circle**:
The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
4. **Ellipse**:
The standard form of the equation of an ellipse with center \((h, k)\), semi-major axis \(a\), and semi-minor axis \(b\) is:
\[
\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1
\]
5. **Hyperbola**:
The standard form of the equation of a hyperbola with center \((h, k)\), and semi-major axis \(a\) and semi-minor axis \(b\) is:
\[
\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1
\]
or
\[
\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1
\]
Each of these formulas represents different types of curves or shapes in a 2D coordinate system.