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3 years ago

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

1 answer:

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

(x-0)2+(y-p)2 = (y+p)2+(x-x)2.
x2+(y-p)2 = (y+p)2.If we expand all the terms and simplify, we obtainx2 = 4py.

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

x2 = 4py.The graph of the parabola would be the reflection, across the x 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".

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

y2 = 4pxwhere the directrix is the verical line 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.

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21 Last year Chelsea and Sonya took 236 pictures during Thanksgiving. This year Chelsea and Sonya each took the same amount of p

Leokris [45]

Let 'c' represent the number of pictures Chelsea took.

Let 's' represent the number of pictures Sonya took.

For last year's Thanksgiving, c + s = 236

For this year's Thanksgiving, let 'x' represent the number of photos taken in total. x = c + s, where c and s are two integers that are the same (c = s).

And we know that for both years, c + s + x = 500.

As we know that c + s is already 236 from last year, we can remove c + s from the equation in bold and replace it with 236 instead.

236 + x = 500.

Now we have to isolate the x term.

x = 500 - 236

x = 264.

We know that x = c + s, where c and s are the same, so we can just use one of the variables and double it (so you either get 2c or 2s - it doesn't matter which one you pick because they're both the same).

2c = 264

c = 132

c = s

s = 132.

Both took 132 pictures this year.

4 0

3 years ago

A 6 foot tall football player casts a 16 inch shadow at the same time stadium we discussed at six for shadow how tall the bleach

katrin [286]

You need to use a ratio of height (H) to shadow length (L) to solve the first problem. It's basically a use of similar triangles, with two perpendicular sides, and with the shadow making the same angle with the vertical.

6 ft = 72 ins, so that rH/L = 72/16 = 9/2 for the player.

So the bleachers are 9/2 x 6 ft = 27 ft.

For the second problem, 9 ft = 108 in, so that the ratio of the actual linear dimensions to the plan's linear dimensions are 9ft/(1/2in) = 2 x 108 = 216.

So the stage will have dimensions 216 times larger than 1.75" by 3".

That would be 31ft 6ins x 54ft.

Live long and prosper.

5 0

3 years ago

1. What percent of 58 is 18?

malfutka [58]

In order to find the answer you will have too divide 58 by 18 and then divide what you get from that by 100 to get your answer.

100%/x%=58/18

(100/x)*x=(58/18)*x

100=3.22222222222*x

(3.22222222222) to get x

100/3.22222222222=x

x=31.0344827586

Therefore your answer is "31%."

Hope this helps.

8 0

3 years ago

(04.01 MC)

Reil [10]

Answer:

144'

Step-by-step explanation:

Your ratio is 45'/5" or 9:1

9x4"=36'

9x3"=27'

45+36+36+27=144'

I believe this is the same answer as I gave previously.

4 0

3 years ago

The volume of a drop of a certain liquid is 0.000047 liter. Write the volume of the drop of a liquid in a scientific notation.

Llana [10]

The answer is 4.7 x 10^-4
If you move the decimal to the right, the exponent will be negative. If you move it to the left, the exponent will be positive.

5 0

3 years ago