1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nitella [24]
3 years ago
6

How would you determine the axis of symmetry in order to graph x^2 = 8y^2.

Mathematics
1 answer:
Tanya [424]3 years ago
5 0
The picture illustrates the definition. The point P is a typical point on the parabola so that its distance from the directrix, PQ, is equal to its distance from F, PF. The point marked V is special. It is on the perpendicular line from F to the directix. This line is called the axis of symmetry of the parabola or simply the axis of the parabola and the point V is called the vertex of the parabola. The vertex is the point on the parabola closest to the directrix.

Finding the equation of a parabola is quite difficult but under certain cicumstances we may easily find an equation. Let's place the focus and vertex along the y axis with the vertex at the origin. Suppose the focus is at (0,p). Then the directrix, being perpendicular to the axis, is a horizontal line and it must be p units away from V. The directrix then is the line y=-p. Consider a point P with coordinates (x,y) on the parabola and let Q be the point on the directrix such that the line through PQ is perpendicular to the directrix. The distance PF is equal to the distance PQ. Rather than use the distance formula (which involves square roots) we use the square of the distance formula since it is also true that PF2 = PQ2. We get

<span>(x-0)2+(y-p)2 = (y+p)2+(x-x)2. 
x2+(y-p)2 = (y+p)2.</span>If we expand all the terms and simplify, we obtain<span>x2 = 4py.</span>

Although we implied that p was positive in deriving the formula, things work exactly the same if p were negative. That is if the focus lies on the negative y axis and the directrix lies above the x axis the equation of the parabola is

<span>x2 = 4py.</span><span>The graph of the parabola would be the reflection, across the </span>x<span> axis of the parabola in the picture above. A way to describe this is if p > 0, the parabola "opens up" and if p < 0 the parabola "opens down".</span>

Another situation in which it is easy to find the equation of a parabola is when we place the focus on the x axis, the vertex at the origin and the directrix a vertical line parallel to the y axis. In this case, the equation of the parabola comes out to be

<span>y2 = 4px</span><span>where the directrix is the verical line </span>x=-p and the focus is at (p,0). If p > 0, the parabola "opens to the right" and if p < 0 the parabola "opens to the left". The equations we have just established are known as the standard equations of a parabola. A standard equation always implies the vertex is at the origin and the focus is on one of the axes. We refer to such a parabola as a parabola in standard position.

Parabolas in standard positionIn this demonstration we show how changing the value of p changes the shape of the parabola. We also show the focus and the directrix. Initially, we have put the focus on the y axis. You can select on which axis the focus should lie. Also you may select positive or negative values of p. Initially, the values of p are positive. 

You might be interested in
Which of the following equations could be used to solve the given equation? 9x + 26 + 7x - 17 = 2x + (-3x) + 5x
gavmur [86]

\left(\mathrm{Decimal:\quad }x=-0.75\right)



hope it helps :P


4 0
3 years ago
Read 2 more answers
(02.04 MC)
borishaifa [10]

Answer:

umm idk let me get back to you

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Somebody please help asapppppp
anzhelika [568]
The function was moved two units to the left (a)
8 0
3 years ago
What is the greatest common factor of the terms in the polynomial 8xt – 4х – 18x??
mariarad [96]

2x

so...

2x (4t - 2 - 9)

2x (4t -  11)

Hope this helped!

~Just a girl in love with Shawn Mendes

3 0
3 years ago
Read 2 more answers
A card game is being played and the 4 of hearts, 8 of clubs, and 9 of hearts
Margaret [11]
B. 32.6%..............
7 0
3 years ago
Read 2 more answers
Other questions:
  • Answers please! will make you brainliest!
    7·2 answers
  • The cone shown has a diameter of 18 meters and a slant height of 15 meters .Which choice is closest to the lateral surface area?
    5·1 answer
  • You work at a fruit stand that sells apples for $2 per pound, oranges for $5 per pound, and bananas for $3
    8·1 answer
  • A rectangle measures 12 cm by 4 cm what is the area
    8·1 answer
  • how do graphs of y=1/x and y=5/(x+6) compare? I know the second graph shifts to left by 6 units but does it move down and how ma
    15·1 answer
  • The temperature is 60°F. The temperature will decrease by 3°F each hours. Let h be the number of hours. When will the temperatur
    8·1 answer
  • A snack company can pack 12 granola bars in a box. How many boxes are needed for 600 granola bars?
    7·1 answer
  • A box contains 10 balls, of which 3 are red, 2 are yellow, and 5 are blue. Five balls are randomly selected with replacement. Ca
    10·1 answer
  • The figure shows ΔDEF and ΔD'E'F'. Fill in each entry box with the answer.
    9·1 answer
  • Do your best i need it quickly sorta, if you do a weird answer just for the points i will report you.
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!