# Given the relation $x^2-4x+y^2-4y+4=0$ determine the following… verify answers

a) The equation of the secant line through the intercepts.

For this part I got $y=-x+2$ as the equation of the secant line

b) The slope of the curve at any point on the curve.

Here I got $\frac{dy}{dx}=-\frac{x-2}{y-2}$

c) The equation of the tanget to the curve where $x=4$

Here's where I'm stuck, because when $x=4, y=2$ and if you plug in 2 for $y$ in the previous formula then you're dividing by 0.

-
The tangent line is vertical. – André Nicolas May 2 '13 at 5:00

The calculations are fine. As you point out, $\frac{dy}{dx}$ does not exist at $y=2$. Sometimes one says the slope is infinite there.
It may be useful to complete the square, getting $(x-2)^2+(y-2)^2=4$. This is a circle centre $(2,2)$, radius $2$. The tangent line at $x=4$ is vertical, so has equation $x=4$.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://math.stackexchange.com/questions/378980/given-the-relation-x2-4xy2-4y4-0-determine-the-following-verify-answers", "fetch_time": 1467053005000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2016-26/segments/1466783396106.25/warc/CC-MAIN-20160624154956-00118-ip-10-164-35-72.ec2.internal.warc.gz", "warc_record_offset": 192181759, "warc_record_length": 16716, "token_count": 277, "char_count": 868, "score": 3.8125, "int_score": 4, "crawl": "CC-MAIN-2016-26", "snapshot_type": "latest", "language": "en", "language_score": 0.8710302114486694, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00009-of-00064.parquet"}