हिन्दी में पढ़ेंHome › Formulas › Ellipse x²/a² + y²/b² = 1 (a > b) › Tangent at (x₁, y₁)
Tangent at (x₁, y₁)
xx₁/a² + yy₁/b² = 1
Where: a = Tangent at (x₁, y₁), b = b, x = x, x₁ = x₁, y = y, y₁ = y₁
Solved example
Given: b = 7, x = 5, x_1 = 10, y = 4, y_1 = 3
Find: a (Tangent at (x₁, y₁))
- Formula: y·y₁/b² + x·x₁/a² = 1
- Rearranged for a: a = b·√(x·x₁/(b² - y·y₁))
- Substitute the values: a = 7·√(10·5/(-3·4 + 7²))
- Rearranged for a: a = -b·√(x·x₁/(b² - y·y₁))
- Substitute the values: a = -7·√(10·5/(-3·4 + 7²))
- Result: a = 8.137335 ; a = -8.137335
Answer: a = 8.137335
Calculator
How to calculate Tangent at (x₁, y₁)
- Write down the formula: xx₁/a² + yy₁/b² = 1.
- Note the known values (b, 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 xx₁/a² + yy₁/b² = 1, where a = Tangent at (x₁, y₁), b = b, x = x, x₁ = x₁, y = y, y₁ = y₁.
What is Tangent at (x₁, y₁) when b = 7, x = 5, x_1 = 10, y = 4, y_1 = 3?
a = 8.137335. Substitute the values into xx₁/a² + yy₁/b² = 1 and simplify.