Question

Obtain the equation of the circle for which (3, 4) and (2, -7) are the ends of a diameter.

Answer 1

The equation of a circle with (x₁, y₁) and (x₂, y₂) as end points of a diameter is

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

Here the end points of a diameter are (3, 4) and (2, –7)

So equation of the circle is (x – 3)(x – 2) + (y – 4) (y + 7) = 0

x² – 2x  – 3x + 6 + y² + 7y – 4y – 28 = 0 

x² + y² – 5x + 3y – 22 = 0