Question

Find the equation of the circle, the coordinates of the end points of whose diameter are (–1, 2) and (4, –3).

Answer 1

We know that the equation of the circle described on the line segment joining (x₁ , y₁) and (x₂ , y₂) as a diameter is (x – x₁) (x – x₂) + (y – y₁) (y – y₂) = 0. 

Here, x₁ = –1, x₂ = 4, y₁ = 2 and y₂ = –3. 

So, the equation of the required circle is (x + 1) (x – 4) + (y – 2) (y + 3) = 0 

⇒ x² + y² – 3x + y – 10 = 0.