- #1
schooler
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Find equation for center at (1,2) and vertex at (1,8) and Minor axis length of 4?
Find equation of the ellipse with center (1,2),
and vertex at (1,8) and minor axis length of 4.
|
| *(1,8)
| :
| :
| :6
| :
| : 2
* . | . + . . . *
| :(1,2)
- - - + - : - - - - -
| :
| :
| :
| *
|schooler said:Find equation for center at (1,2) and vertex at (1,8) and Minor axis length of 4?
This should besoroban said:[tex]\frac{(x-1)^2}{4} + \frac{(y-2)^2}{36} \;=\;1[/tex]
An ellipse is a type of geometric shape that is similar to a circle, but has two distinct focal points instead of one. It is formed by the intersection of a cone and a plane, resulting in a curved oval shape.
To find the equation of an ellipse with given points and minor axis length, you can use the standard form of the equation: (x-h)^2/a^2 + (y-k)^2/b^2 = 1. Here, (h,k) represents the coordinates of the center of the ellipse, a represents the length of the semi-major axis, and b represents the length of the semi-minor axis. You can then plug in the given points and minor axis length to solve for the remaining variables and determine the equation.
The given points represent two points on the ellipse's circumference. These points, along with the center point, determine the size and orientation of the ellipse.
The minor axis length in an ellipse is measured as the distance between the two furthest points on the ellipse's shorter axis. It is also known as the semi-minor axis length, as it is half of the total length of the minor axis.
Yes, the equation of an ellipse can also be written in the general form Ax^2 + By^2 + Cxy + Dx + Ey + F = 0, where A, B, and C represent the coefficients of the x^2, y^2, and xy terms, respectively. However, the standard form is the most commonly used and easier to work with.