Question

A(1, –2) is a point on the circle (x – 3)^2+ (y + 1)^2= 5. State the coordinates of the centre of the circle and hence find the coordinates of the point B, where AB is a diameter of the circle

Answer 1

Step-by-step explanation:

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=4−31 + 2y

1 +4 =3 y

1 =6-4 y

1 =2

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