Diameter form

(x − x₁)(x − x₂) + (y − y₁)(y − y₂) = 0

Where: x = Diameter form, x₁ = x₁, x₂ = x₂, y = y, y₁ = y₁, y₂ = y₂

Given: x_1 = 5, x_2 = 10, y = 4, y_1 = 3, y_2 = 8
Find: x (Diameter form)

1. Formula: (x - x₁)·(x - x₂) + (y - y₁)·(y - y₂) = 0
2. Rearranged for x: x = x₁/2 + x₂/2 - √(x₁² - 2·x₁·x₂ + x₂² - 4·y² + 4·y·y₁ + 4·y·y₂ - 4·y₁·y₂)/2
3. Substitute the values: x = 10/2 + 5/2 - √(10² - 2·10·5 + 4·3·4 - 4·3·8 - 4·4² + 4·4·8 + 5²)/2
4. Rearranged for x: x = x₁/2 + x₂/2 + √(x₁² - 2·x₁·x₂ + x₂² - 4·y² + 4·y·y₁ + 4·y·y₂ - 4·y₁·y₂)/2
5. Substitute the values: x = 10/2 + 5/2 + √(10² - 2·10·5 + 4·3·4 - 4·3·8 - 4·4² + 4·4·8 + 5²)/2
6. Result: x = 4.298438 ; x = 10.701562

Answer: x = 4.298438

What is the formula for Diameter form?

The formula is (x − x₁)(x − x₂) + (y − y₁)(y − y₂) = 0, where x = Diameter form, x₁ = x₁, x₂ = x₂, y = y, y₁ = y₁, y₂ = y₂.

What is Diameter form when x_1 = 5, x_2 = 10, y = 4, y_1 = 3, y_2 = 8?

x = 4.298438. Substitute the values into (x − x₁)(x − x₂) + (y − y₁)(y − y₂) = 0 and simplify.