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General equation
ax² + 2hxy + by² + 2gx + 2fy + c = 0
Where: a = General equation, b = b, c = y-intercept, f = f, g = g, h = h, x = x, y = y
Solved example
Given: b = 7, c = 5, f = 10, g = 4, h = 3, x = 8, y = 6
Find: a (General equation)
- Formula: a·x² + b·y² + c + 2·f·y + 2·g·x + 2·h·x·y = 0
- Rearranged for a: a = (-b·y² - c - 2·f·y + 2·x·(-g - h·y))/x²
- Substitute the values: a = (-2·10·6 - 5 - 6²·7 + 2·8·(-3·6 - 4))/8²
- Result: a = -11.390625
Answer: a = -11.390625
Calculator
How to calculate General equation
- Write down the formula: ax² + 2hxy + by² + 2gx + 2fy + c = 0.
- Note the known values (b, c, f, g, h, x, y).
- Substitute them and simplify to find a.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for General equation?
The formula is ax² + 2hxy + by² + 2gx + 2fy + c = 0, where a = General equation, b = b, c = y-intercept, f = f, g = g, h = h, x = x, y = y.
What is General equation when b = 7, c = 5, f = 10, g = 4, h = 3, x = 8, y = 6?
a = -11.390625. Substitute the values into ax² + 2hxy + by² + 2gx + 2fy + c = 0 and simplify.