Question

If the coordinates of one end of a diameter of the circle x² + y² – 4x – 6y + 11 = 0 are (3, 4), then the coordinates of the other end are __________.

Answer 1

Since equation of circle is
x² + y² – 4x – 6y + 11 = 0
i.e. center of circle is (2, 3)
also, given co-ordinate of are end of diameter is (3, 4) we know, center of a circle is mid point of the diameter,

Let (a, b) the other end of the diameter

$$\begin{gathered} \therefore \frac{a+3}{2}=2 \\ \frac{b+4}{2}=3 \\ \Rightarrow a=1\mathrm{and}b=2 \end{gathered}$$
Hence, co-ordinate of other end of diameter are (1, 2)