Just as we can write the equation for an ellipse given its graph, we can graph an ellipse given its equation. To graph ellipses centered at the origin, we use the standard form
for horizontal ellipses and
for vertical ellipses.
Given the standard form of an equation for an ellipse centered at
sketch the graph.
Use the standard forms of the equations of an ellipse to determine the major axis, vertices, co-vertices, and foci.
If the equation is in the form
where
then
the major axis is the
x -axis
the coordinates of the vertices are
the coordinates of the co-vertices are
the coordinates of the foci are
If the equation is in the form
where
then
the major axis is the
y -axis
the coordinates of the vertices are
the coordinates of the co-vertices are
the coordinates of the foci are
Solve for
using the equation
Plot the center, vertices, co-vertices, and foci in the coordinate plane, and draw a smooth curve to form the ellipse.
Graphing an ellipse centered at the origin
Graph the ellipse given by the equation,
Identify and label the center, vertices, co-vertices, and foci.
First, we determine the position of the major axis. Because
the major axis is on the
y -axis. Therefore, the equation is in the form
where
and
It follows that:
the center of the ellipse is
the coordinates of the vertices are
the coordinates of the co-vertices are
the coordinates of the foci are
where
Solving for
we have:
Therefore, the coordinates of the foci are
Next, we plot and label the center, vertices, co-vertices, and foci, and draw a smooth curve to form the ellipse. See
[link] .
Graphing an ellipse centered at the origin from an equation not in standard form
Graph the ellipse given by the equation
Rewrite the equation in standard form. Then identify and label the center, vertices, co-vertices, and foci.
First, use algebra to rewrite the equation in standard form.
Next, we determine the position of the major axis. Because
the major axis is on the
x -axis. Therefore, the equation is in the form
where
and
It follows that:
the center of the ellipse is
the coordinates of the vertices are
the coordinates of the co-vertices are
the coordinates of the foci are
where
Solving for
we have:
Therefore the coordinates of the foci are
Next, we plot and label the center, vertices, co-vertices, and foci, and draw a smooth curve to form the ellipse.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life