HELP!! i have a page of math to do and i am SO stuck!?

Question

I have to graph an ellipse and find its foci
how do i do this
ex: 5x*squared* + y*squared* = 25

Answer 1

The general form of an ellipse centered at (h, k) is:

(x - h)²/a² + (y - k)²/b² = 1

(or you swap the a and b if the major axis is along the y-axis instead of the x-axis)

To get your equation in that form, divide both sides by 25:

5x²/25 + y²/25 = 1
x²/5 + y²/25 = 1

So the center is the origin (0,0), and the ellipse is bigger along the y-axis (√25 = 5 units) than along the x-axis (√5 units).

To graph it, you take the center (0, 0) and add and subtract the major and minor axes:

(0 + √5, 0) = (√5, 0)
(0 - √5, 0) = (-√5, 0)
(0, 0 + 5) = (0, 5)
(0, 0 - 5) = (0, -5)

If you draw those points, it should be easy to see how to draw the ellipse.

Now the foci are a little tougher....

The way the foci work are you have to compute another number, c:

c = a² - b²

Since a = 5 (a's always bigger than b) and b = √5:

c² = 5² - (√5)² = 25 - 5 = 20

So c = √20 = √(4x5) = √4√5 = 2√5

Then the rule to find the foci is to add and subtract c from the center along the major axis (y, in this case):

(0, 0 + 2√5) = (0, 2√5)
(0, 0 - 2√5) = (0, -2√5)

Answer 2

hi there.

let's presume that an asterisk is the square.

5x* + y* = 25

first, you make sure that when u graph an ellipse, make the equation equal to 1.

so.. you'll divide away the 25 on the equation and u'l get, x*/5 + y*/25 = 1

then.. ur center would be (0,0) ,
vertices are
for major we have (0, +- 5)
for minor we have ( +- square root of 5, 0)

notice that i took the squre root of the denominator of both x and y, and the major vertices wud be from the bigger denominator, depending on the given.

ok. so.. just plot the following numbers we got from the vertices and the center. trace the following vertices and there you have your ellipse figure.

and then you look for the foci..

foci is..

(0, +- square root of 20) which shud be rewritten as
f (0, +- 2 square root of 5)

wherd i get 20? just simply subtract the bigger denominator with the smaller one. and then take its square root. =)

ok.. then.. what you have to do when u have square roots like that is to use the calculator, and just type it in. then ul get the aproximate amount of number which then u shud include on ur graph..

Foci are just 2 tiny dots near the major vertices. that's all u hav to do to plot them on ur graphs.

hm.. i hope it was clear.
goodluck =) just ask me for further questions. id be glad to xplain. =) hahaha