A circle $C\,$ has centre $(3, 1)$ and radius $5\sqrt{5}$ . 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 $m^2 + 1)x^2 - (2m + 6)x + 5 = 0$ .

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

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

A circle $C\,$ has centre $(3, 1)$ and radius $5\sqrt{5}$ . 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 $m^2 + 1)x^2 - (2m + 6)x + 5 = 0$ .

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

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

Circles

Circles Questions