9758/2022/P1/Q05

The line with equation $y=m x$ is a tangent to the curve with equation
$$(x+8)^2+(y-14)^2=52 .$$
(a) Show that $m$ satisfies the equation
$$3 m^2+56 m+36=0 \text {. }$$

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$A$ and $B$ are points on the curve. The tangent at $A$ and the tangent at $B$ intersect at the origin.
(b) Find the coordinates of $A$ and $B$.

[4]