Straight line $L: 2x - y +k = 0$ is the tangent of a circle $C_1: x^2 +y^2 = 5$ , if $k <0$, What is the shortest distance between $L$ and another circle $C_2: (x+6)^2 + (y+2)^2 = 9$?
$3$
$3(5)^{\frac{1}{2}}$
$3(5)^{\frac{1}{2}} - 3$
$3(5)^{\frac{1}{2}} + 3$
1) The center of $C_1$ is at $O(0, 0)$.
2) Let $R$ be the line parallel to $L: 2x – y + k = 0$ and passing through $O$. Find the equation of $R$.
3) Let $N$ be the line normal to $R$ and passes through $O$. Find the equation of $N$.
4) Find the points of tangency $K_1$ and $K_2$. Show that $K_2$ should be rejected.
5) If $L$ cuts the y-axis at $P$, then $OP =?$
6) Find $J$. From which, $QJ =?, QP =?$ And therefore $JP = ?$