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Tangent at (x₁, y₁)
yy₁ = 2a(x + x₁)
Where: a = Tangent at (x₁, y₁), x = x, x₁ = x₁, y = y, y₁ = y₁
Solved example
Given: x = 7, x_1 = 5, y = 10, y_1 = 4
Find: a (Tangent at (x₁, y₁))
- Formula: y·y₁ = 2·a·(x + x₁)
- Rearranged for a: a = y·y₁/(2·(x + x₁))
- Substitute the values: a = 10·4/(2·(5 + 7))
- Result: a = 1.666667
Answer: a = 1.666667
Calculator
How to calculate Tangent at (x₁, y₁)
- Write down the formula: yy₁ = 2a(x + x₁).
- Note the known values (x, x₁, y, y₁).
- Substitute them and simplify to find a.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Tangent at (x₁, y₁)?
The formula is yy₁ = 2a(x + x₁), where a = Tangent at (x₁, y₁), x = x, x₁ = x₁, y = y, y₁ = y₁.
What is Tangent at (x₁, y₁) when x = 7, x_1 = 5, y = 10, y_1 = 4?
a = 1.666667. Substitute the values into yy₁ = 2a(x + x₁) and simplify.