Parabola!!

For the parabola $$x^2+4y^2-4xy-10x+5=0$$, find the equation of tangent at vertex and equation of axis of parabola?

5 years, 1 month ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

This is an interesting problem, namely because the parabola's axis is not parallel to an x-y axis. We are used to dealing with conics in this form. However, using the definition of a parabola (distance to a point on the parabola is the same from a fixed point called the focus and a fixed line called the directrix), one can develop a hairy formula for a general parabola. Plugging in and solving for some variables, I got a possible focus to be (1,0) and a possible directrix of x-2y=0. The axis of the parabola then must be 2x+y=2, and the vertex (9/10,7/10). There could be more answers, but I didn't check. If you want me to look more into this problem or write a formal proof, I'll consider it.

- 5 years, 1 month ago

your in level four of geometry...please give it a try at least....it does not need much perspiration...best of luck ....:)

- 5 years, 1 month ago

Dude this is already done... but i liked this problem very much that's why posted that..

- 5 years, 1 month ago
{"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": 1, "mathjax_asciimath": 1, "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}