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Length of tangent
√S₁ = √(x₁² + y₁² + 2gx₁ + 2fy₁ + c)
Where: S₁ = Length of tangent, c = y-intercept, fy₁ = fy₁, gx₁ = gx₁, x₁ = x₁, y₁ = y₁
Solved example
Given: c = 7, fy_1 = 5, gx_1 = 10, x_1 = 4, y_1 = 3
Find: S_1 (Length of tangent)
- Formula: √(S₁) = √(c + 2·fy₁ + 2·gx₁ + x₁² + y₁²)
- Rearranged for S₁: S₁ = c + 2·fy₁ + 2·gx₁ + x₁² + y₁²
- Substitute the values: S₁ = 2·10 + 3² + 4² + 2·5 + 7
- Result: S₁ = 62
Answer: S_1 = 62
Calculator
How to calculate Length of tangent
- Write down the formula: √S₁ = √(x₁² + y₁² + 2gx₁ + 2fy₁ + c).
- Note the known values (c, fy₁, gx₁, x₁, y₁).
- Substitute them and simplify to find S_1.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Length of tangent?
The formula is √S₁ = √(x₁² + y₁² + 2gx₁ + 2fy₁ + c), where S₁ = Length of tangent, c = y-intercept, fy₁ = fy₁, gx₁ = gx₁, x₁ = x₁, y₁ = y₁.
What is Length of tangent when c = 7, fy_1 = 5, gx_1 = 10, x_1 = 4, y_1 = 3?
S_1 = 62. Substitute the values into √S₁ = √(x₁² + y₁² + 2gx₁ + 2fy₁ + c) and simplify.