6.2 Equation of a Circle

The circle $C\,$ has the equation

x^2+y^2+8x-4y+k=0,

where $k\,$ is a constant. Given that the point $(1, 5)$ lies on $C$ .

a.

Find the value of $k$ .

[2]

b.

Find the coordinates of the centre and the radius of $C$ .

[3]

c.

A straight line that passes through the point $A (3, 7)$ is tangent to the circle $C\,$ at the point $B$ .

Find the exact length of the line $A B$ .

[5]

6.2 Equation of a Circle

The circle $C\,$ has the equation

x^2+y^2+8x-4y+k=0,

where $k\,$ is a constant. Given that the point $(1, 5)$ lies on $C$ .

a.

Find the value of $k$ .

[2]

b.

Find the coordinates of the centre and the radius of $C$ .

[3]

c.

A straight line that passes through the point $A (3, 7)$ is tangent to the circle $C\,$ at the point $B$ .

Find the exact length of the line $A B$ .

[5]

6.2 Equation of a Circle

6.2 Equation of a Circle Questions