# Align lower lines of a set of equations at an extra point

I have a series of equations which I want to align at the equals sign. However I also wish for the left side of the last three lines to be left-aligned with each other (i.e. aligned to the widest of the three, not aligned flush to the left edge of the page).

Here's what I have currently:

Here's what I'd like:

My code is as follows:

\begin{align*}
\text{Solve } D_1 = D_2 \Rightarrow \sqrt{(x-3)^2 + (y-4)^2} &= \sqrt{(y-2)^2}\\
(x-3)^2 + (y-4)^2 &= \quad (y-2)^2\\
(x^2 - 6x + 9) + (y^2 - 8y + 16) &= \quad y^2 - 4y + 4\\
x^2 - 6x + 21 &= \quad 4y\\
x^2 - 6x - 4y + 21 &= \quad 0
\end{align*}


It seems that what I'd like is an extra alignment point for the last 3 rows, but I haven't been able to find anything like that.

I've seen the aligned environment, but I believe that would break the alignment of the equals signs.

Any ideas?

With array environment:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
$\setlength\arraycolsep{1pt} \begin{array}{rll} \text{Solve } D_1 & = D_2 \Rightarrow \sqrt{(x-3)^2 + (y-4)^2} & = \sqrt{(y-2)^2} \\ &\hfill (x-3)^2 + (y-4)^2 & = \quad (y-2)^2 \\ & (x^2 - 6x + 9) + (y^2 - 8y + 16) & = \quad y^2 - 4y + 4 \\ & x^2 - 6x + 21 & = \quad 4y\\ & x^2 - 6x - 4y + 21 & = \quad 0 \end{array}$
\end{document}


The alignment seems very confusing but ...

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\newlength\zzz
\settowidth\zzz{$\displaystyle x^2 - 6x + 9) + (y^2 - 8y + 16)$}

\begin{align*}
\text{Solve } D_1 = D_2 \Rightarrow \sqrt{(x-3)^2 + (y-4)^2} &= \sqrt{(y-2)^2}\\
(x-3)^2 + (y-4)^2 &= \quad (y-2)^2\\
(x^2 - 6x + 9) + (y^2 - 8y + 16) &= \quad y^2 - 4y + 4\\
\makebox[\zzz][l]{$\displaystyle x^2 - 6x + 21$} &= \quad 4y\\
\makebox[\zzz][l]{$\displaystyle x^2 - 6x - 4y + 21$} &= \quad 0
\end{align*}

\end{document}

• This looks like the most flexible solution, layout wise. Unfortunately the necessary commands aren't supported in my case (a third party website with MathJax). – Neil Haskins Jul 17 '20 at 16:46
• @NeilHaskins ah well mathjax doesn't use tex so things are different in that case. – David Carlisle Jul 17 '20 at 18:18

I would suggest a slightly different way of computing, and another layout, with the \ArrowBetweenLinescommand from mathtools, which requires using alignat{2}:

\documentclass{article}
\usepackage{mathtools}

\begin{document}

\begin{alignat*}{2}
\intertext{Solve $D_1 = D_2 \Rightarrow$}
& & \sqrt{(x-3)^2 + (y-4)^2} &= \sqrt{(y-2)^2}\\
\ArrowBetweenLines
& & (x-3)^2 + (y-4)^2 & = (y-2)^2\\
\ArrowBetweenLines
& & (x-3)^2 & = (y-2)^2 -(y-4)^2\\
& & & = \bigl((y-2)-(y-4)\bigr)\bigl((y-2) + (y-4)\bigr)\\
\ArrowBetweenLines
& &x^2 - 6x + 9 & = 2 (2y -6)\\
\ArrowBetweenLines
& & x^2 - 6x - 4y + 21 &= 0
\end{alignat*}

\end{document}