Example 1 Sketch
the graph of each of the following ellipses.
Sumber
Solution
(a) So,
the center of this ellipse is (−2, 4) and as usual be
careful with signs here! Also, we have a = 3 and b = 5 .
So, the points are,
right most
point : (1, 4)
left most point
: ( – 5, 4)
top most point
: ( – 2, 9)
bottom
most point : ( – 2, – 1)
Here is a sketch of this ellipse.
(b) The
center for this part is (0,3) and we have a
= 7 and b = 2 . The points
we need are,
right most
point : (7, 3)
left most point
: (– 7, 3)
top most point
: (0, 5)
bottom most
point : (0, 1)
Here is the sketch of this ellipse.
(c) Now
with this ellipse we’re going to have to be a little careful as it isn’t quite
in standard form yet. Here is the standard form for this ellipse.
Note
that in order to get the coefficient of 4 in the numerator of the first term we
will need to have a ¼ in the
denominator. Also, note that we don’t even have a fraction for the y term.
This implies
that there is in fact a 1 in the denominator. We could put this in if it would
be helpful to see what is going on here.
So,
in this form we can see that the center is (−1, −3) and that a = ½ and b
= 1. The points
for this ellipse are,
right most
point : 
left most point
: 
top most point
: ( – 1, – 2)
bottom most
point : ( – 1, – 4)
Here is this ellipse.
Sumber
Labels:
Mathematician
Thanks for reading Ellipses – Example. Please share...!
