—(••÷[ roтaтιng conιc ѕecтιonѕ ]÷••—

Salutations, guests of Mathland!

We will be upon our destination of the Mad Hatter's Tea Party in a few seconds!

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I most humbly welcome you!

Today at the party we will be discussing the rotation of conic sections, otherwise known as "Axis Rotation".

Here are some notes regarding this process:

As demonstrated by the image above, in order to start, we must determine and match the coefficients with that of the first equation,  Second, we plug it into the equation and find what cot2(θ) is equal to. Next, we are able to replace the x with x' (x-prime) and y with y' (y-prime) in order to determine the coordinates on the rotated Cartesian Plane. Finally we plus it into the original equation and use algebra to simplify it.

Here is an example:

That is all! 

I do hope you enjoyed your time and our lovely conversation at the tea party! 

The March Hare seems to have enjoyed our company, for he tells us to visit again soon.

Farewell for now!

See you next time, lovely guests.~

••.•´¯`•.•• ραяαвσℓαѕ ••.•´¯`•.••

Greetings, visitors of Mathland.~

How have you all been? I have been quite lovely myself. Today, I will be taking you all on a tour through the woods to go visit the March Hare at the Mad Hatter's tea party. Along the way, I will be reviewing the concepts of Parabolas and its equations with you all.

Starting off, the base equation for parabolas is:

(x-h)_­­­_­² = 4c (y-k)

Therefore:

Vertex: (h,k)

Focus: (h, k+c)

Directrix: y=k-c

A.O.S: x=h

In order to find the "c" value in this equation, one merely sets the number in the place of "4c" equal to '4c' and solve for "c". If the "c" is greater then zero, then the graph is facing upward. However, if the "c" is less then zero, then the graph is facing downwards.

Notes:

On the other hand, if the graph is opening to the left or right, the equation switches. It changes to:

(y-kh)_­­­_­² = 4c (x-h)

Meaning:

Vertex: (h,k)

Focus: (h+c, k)

Directrix: y=h-c

A.O.S: y=k

Notes:

To find the "c" of this equation, it is still the same exact process as finding the "c" of the other equation. Only in this situation, if c is greater then zero, then the graph opens right. I fc is less then zero, then the graph opens left.

That will be all for today!~ 

We will soon arrive at the Tea Party.~

See you next time.~

•´¯`•. 2nd ѕeмeѕтer goalѕ .•´¯`•

Welcome back, dear guests of Mathland~

Forgive me, for I took a few weeks journey to the Clover Kingdom that situates itself north of the Heart Kingdom of the Red Queen.~

I hope you all have had a lovely Christmas break?

There are a few things I wanted to touch on as I have received fantastic advice from the Emerald Queen in the Kingdom of Clover during my visit. 

She recommends that I improve upon my tendency to procrastinate, as well as my manner to which I proceed with my work. Also, she recommends that I work on studying more as it will benefit me greatly. 

However, along with all such advice, she did in fact say that I have done well in the categories of being able to keep up with the workload and the classes, along with the memorization of formulas.

Ah, might I also regale you dear guests with a tale from my break?~

During such a lovely relaxing vacation, I was able to catch up on my lack of sleep - just a bit.~ 

I usually slept around 3-4 in the morning and awoke around noon. In addition to such, I usually fell asleep while talking with friends through what some refer to as "Skype".~ 

Quite an interesting experience I might say.~

Well that is all, I do hope you all enjoyed this first post of the new 2015 year.~