这里允许练习latex吧

manthanein

\(x^{2}+y^{2}\lt r^{2}+2(ax+by)-(a^{2}+b^{2})\)
\((a^{2}+b^{2})(x^{2}+y^{2})\lt (a^{2}+b^{2})r^{2}+2(a^{2}+b^{2})(ax+by)-(a^{2}+b^{2})^{2}\)
\((a^{2}+b^{2})(x^{2}+y^{2})\lt (a^{2}+b^{2})(r^{2}-a^{2}-b^{2})+2(a^{2}+b^{2})(ax+by)\)

manthanein

\((ax+by)^{2}-2(a^{2}+b^{2})(ax+by)\lt (a^{2}+b^{2})(r^{2}-a^{2}-b^{2})-(ay-bx)^{2}\)
\((ax+by)^{2}-2(a^{2}+b^{2})(ax+by)+(a^{2}+b^{2})^{2}\lt (a^{2}+b^{2})r^{2}-(ay-bx)^{2}\)
\((ax+by-a^{2}-b^{2})^{2}\lt (a^{2}+b^{2})r^{2}-(ay-bx)^{2}\)

TSC999

r2+(a2+b2)+2a2+b2−−−−−−√r>(x−a)2+(y−b)2
(a2+b2−−−−−−√+r)2>(x−a)2+(y−b)2

gxqcn

论坛已自带 \(\rm\LaTeX\) 预览功能，在发帖回帖提交之前可先预览效果，平时也可利用该功能练习，没必要专门开贴试验练习。

manthanein

给定曲线\(F(x,y)=0\)
在曲线上有一点\((x_0,y_0)\),\(F(x_0,y_0)=0\)
另外有一点\((p,q)\)，\(F(p,q)=0\)
有一条过点\((x_0,y_0)\)的直线\(xcos\alpha+ysin\alpha-P=0\)，\(x_0cos\alpha+y_0sin\alpha-P=0\)

manthanein

\(\displaystyle \lim_{\sqrt{(p-x_0)^2+(q-y_0)^2} \to 0} (pcos\alpha+qsin\alpha-P)=0\)

manthanein

\(\displaystyle \lim_{(p-x_0)^2+(q-y_0)^2 \to 0} (pcos\alpha+qsin\alpha-P)=0\)