Question

find the equation of the circle whose diameter is the join of the point X1 Y1 and X2 Y2

Answer 1

we have to find the equation of circle whose diameter is join of the point (x₁,y₁) and (x₂, y₂) .
Let A ≡ (x₁,y₁) and B ≡ (x₂,y₂)
Then, equation of circle is given by
(x - x₁)(x - x₂) +(y - y₁)(y - y₂) = 0 [ by formula ]
x² - (x₁ + x₂)x + x₁x₂ + y² - (y₁ + y₂)y + y₁y₂ = 0
x² + y² -(x₁ + x₂)x - (y₁ + y₂)y + x₁x₂ + y₁y₂ = 0

Hence, the equation of circle is x² + y² -(x₁ + x₂)x - (y₁ + y₂)y + x₁x₂ + y₁y₂ = 0

Answer 2

In the attachment I have answered this problem.

The detailed derivation of the equation is done step by step.

I hope this answer help you