Homework Help: When we use standerd Equation of an ellipse

1. Apr 21, 2010

r-soy

Hi

when we use standerd Equation of an ellipse

here 2 formula 1 and 2 when we use 1 and when we use 2

hlep me

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2. Apr 21, 2010

CompuChip

Errr... what's the difference, except that a is called b and b is called a in (2)?

3. Apr 21, 2010

r-soy

when we say a is called b and b is called a in the queation

i mean in queation how we nowthe solve will be by formula 1 or 2

help me >>

4. Apr 21, 2010

Staff: Mentor

The two formulas shown in the page you scanned are needlessly complicated. Only one equation is needed for an ellipse.
$$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$

If a > b, the major axis is along the x axis.
If a < b, the major axis is along the y axis.

Ex. 1
$$\frac{x^2}{25} + \frac{y^2}{16} = 1$$
x-intercepts (vertices) at (5, 0) and (-5, 0).
y-intercepts at (0, 4), and (0, -4).
Foci at (3, 0) and (-3, 0).

Ex. 2
$$\frac{x^2}{16} + \frac{y^2}{25} = 1$$
x-intercepts at (4, 0) and (-4, 0).
y-intercepts (vertices) at (0, 5), and (0, -5).
Foci at (0, 3) and (0, -3).

5. Apr 21, 2010

iRaid

The b2 and a2 (depending on position) tell you the major and minor axis and which way to ellipse will be (like vertical or horizontal)

keep in mind: a cannot equal b because then it will be a circle not an ellipse.

Last edited: Apr 21, 2010
6. Apr 21, 2010

Staff: Mentor

A circle can be thought of as a special case of the ellipse, where the major and minor axes are equal.

7. Apr 21, 2010

iRaid

Well yes, but it's generally not.

8. Apr 22, 2010

CompuChip

Ellipses are generally not circles, indeed.
But all circles are ellipses.

Just like not all rectangles are squares, but all squares are rectangles.

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