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Tangent at (x₁, y₁)
xx₁ + yy₁ + g(x + x₁) + f(y + y₁) + c = 0
Where: c = y-intercept, f = f, g = g, x = x, x₁ = x₁, y = y, y₁ = y₁
Solved example
Given: f = 7, g = 5, x = 10, x_1 = 4, y = 3, y_1 = 8
Find: c (y-intercept)
- Formula: c + f·(y + y₁) + g·(x + x₁) + x·x₁ + y·y₁ = 0
- Rearranged for c: c = -f·y - f·y₁ - g·x - g·x₁ - x·x₁ - y·y₁
- Substitute the values: c = -10·4 - 10·5 - 3·7 - 3·8 - 4·5 - 7·8
- Result: c = -211
Answer: c = -211
Calculator
How to calculate Tangent at (x₁, y₁)
- Write down the formula: xx₁ + yy₁ + g(x + x₁) + f(y + y₁) + c = 0.
- Note the known values (f, g, x, x₁, y, y₁).
- Substitute them and simplify to find c.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Tangent at (x₁, y₁)?
The formula is xx₁ + yy₁ + g(x + x₁) + f(y + y₁) + c = 0, where c = y-intercept, f = f, g = g, x = x, x₁ = x₁, y = y, y₁ = y₁.
What is Tangent at (x₁, y₁) when f = 7, g = 5, x = 10, x_1 = 4, y = 3, y_1 = 8?
c = -211. Substitute the values into xx₁ + yy₁ + g(x + x₁) + f(y + y₁) + c = 0 and simplify.