Question

If one end of a diameter of the circle x² + y² – 4x – 6y + 11 = 0 is (3, 4), then find the coordinate of the other end of the diameter

Answer 1

Let the other end of the diameter is (x₁, y₁).

Equation of given circle is x² + y² – 4x – 6y + 11 = 0

Centre = (– g, – f) = (2, 3)

∴ `(x_1 + 3)/2` = 2

⇒ x₁ + 3 = 4

⇒ x₁ =

And `(y_1 + 4)/2` = 3

⇒ y₁ + 4 = 6

⇒ y₁ = 2

Hence, the required coordinates are (1, 2).