6.2 Equation of a Circle

The circle $C\,$ has the equation

x^2+y^2+6x-2y+k=0,

where $k\,$ is a constant. Given that the point $(2, 4)$ lies on $C$ .

A straight line that passes through the point $A (6, 8)$ is tangent to the circle $C\,$ at the point $B$ .

Find the value of $k$ , the coordinates of the centre and the radius of $C$ , and the exact length of the line $A B$ .

[10]

The circle $C\,$ has the equation

x^2+y^2+6x-2y+k=0,

where $k\,$ is a constant. Given that the point $(2, 4)$ lies on $C$ .

A straight line that passes through the point $A (6, 8)$ is tangent to the circle $C\,$ at the point $B$ .

Find the value of $k$ , the coordinates of the centre and the radius of $C$ , and the exact length of the line $A B$ .

[10]

6.2 Equation of a Circle Questions