Finding Equations of Tangents to a Circle Drawn from Origin
The circle ${{C}_{1}}$ has an equation of ${{x}^{2}}+{{y}^{2}}-4x+8y+16=0$.
(a)
Find the centre of another circle which is a reflection of ${{C}_{1}}$ in the line $y=x$.
(b)
Two tangents ${{l}_{1}}$ and ${{l}_{2}}$ are drawn from the origin to the circle ${{C}_{1}}$. Find the equations of the two tangents.
(c)
A circle ${{C}_{2}}$ passes through the point $\left( -2,3 \right)$ and has the same centre as the circle ${{C}_{1}}$. Find the equation of the circle ${{C}_{2}}$ and express it in the general form.
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