Question

If one end of a diameter of the circle $x^2+y^2-4x-6y+11=0$ is $(3,4)$ the the co-ordinates the other end are:

• A. $(1,2)$
• B. $(2,1)$
• C. $(-1,2)$
• D. $Noneofthese$

Answer 1

The correct option is A $(1,2)$

Solution:

Equation of the given circle is $x^2+y^2-4x-6y+11=0$

Hence the centre of the circle is $(2,3)$.

The coordinate of the point which lies on the circle is $(3,4)$

Let the coordinates of the point on the other end of the diameter be $(x_1,y_1)$

The coordinate of midpoint of these two points is $(2,3)$

$x_1=4-3$

$x_1=1$

$\frac{y_1+4}{2}=3$

$y_1=6-4$

$y_1=2$

Hence the coordinates of the point on the other end of the diameter is $(1,2)$