When we use standerd Equation of an ellipse

[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

 

[CompuChip]

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

 

[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 >>

 

[Mark44]

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).

 

[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.

 

[Mark44]

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

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

 

[iRaid]

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

Well yes, but it's generally not.

 

[CompuChip]

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

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