Originally Posted by

**GrigOrig99** Below, I have posted a question and a solution I was provided. The problem is that I don't understand how the part bordered by **AAA** was arrived at. Specifically $\displaystyle \sqrt{m^2+1}$, & why it's simply multiplied against $\displaystyle |3m+4|$? After multiplying that expression, I end up with $\displaystyle (3m^2+24m+16)(m^2+1)=20$, & not $\displaystyle (11m-2)(m-2)=0$. Can anyone help clarify this for me, or is there a better approach?

**Attempt:** Line equation for (2,-2): $\displaystyle y+2=m(x-2)$

From circle equation: centre c = (-1, 2)

Sub c into the line equation: $\displaystyle 2+2=m(-1-2)\rightarrow 3m+4=0$

**AAA**

The distance from the point (-1, 2) to this line is $\displaystyle |3m+4|\sqrt{m^2+1}=2\sqrt{5}$

$\displaystyle (11m-2)(m-2)=0$**AAA**

**Ans.** (From text book): $\displaystyle 2x-y-6=0$ & $\displaystyle 2x-11y-26=0$