1.1. A circle has equation ${x}^{2}+{y}^{2}-12x+14y=-68$.

The lines ${l}_{1}$ and ${l}_{2}$ are both tangents to the circle, and they intersect at the origin.

Explain why the equations for ${l}_{1}$ and ${l}_{2}$ must each be in the form $y=mx$, where $m$ is the gradient of the line.

1.2. Show that the gradients of ${l}_{1}$ and ${l}_{2}$ must be the solutions to the equation

$19{m}^{2}+84m+32=0.$

1.3. Hence find the equations of  ${l}_{1}$ and  ${l}_{2}$, giving your answers in the form $y=mx.$.