1 Pure Mathematics

A circle $C\,$ has centre $(10, 6)$ and radius $2172\sqrt{17}$ . A line $L\,$ has equation $y = m x$ .

Show that the $x$ -coordinate of any points of intersection of $C\,$ and $L\,$ satisfies the equation $m^2 + 1)x^2 - (12m + 20)x + 68 = 0$ .

[4]

Find values of $m\,$ for which the equation in (a) has equal roots.

[4]

Two lines drawn from the origin which are tangents to $C$ . Find the coordinates of the points of contact between the tangents and $C$ .

[4]

1 Pure Mathematics Questions

A circle $C\,$ has centre $(10, 6)$ and radius $2172\sqrt{17}$ . A line $L\,$ has equation $y = m x$ .

Show that the $x$ -coordinate of any points of intersection of $C\,$ and $L\,$ satisfies the equation $m^2 + 1)x^2 - (12m + 20)x + 68 = 0$ .

[4]

Find values of $m\,$ for which the equation in (a) has equal roots.

[4]

Two lines drawn from the origin which are tangents to $C$ . Find the coordinates of the points of contact between the tangents and $C$ .

[4]