Write the standard form equation of the ellipse shown in the graph, and identify the foci.
2 answers:
Answer option A
From the given graph is a Vertical ellipse
Center of ellipse = (-2,-3)
Vertices are (-2,3) and (-2,-9)
Co vertices are (-6,-3) and (2,-3)
The distance between center and vertices = 6, so a= 6
The distance between center and covertices = 4 , so b= 4
The general equation of vertical ellipse is
(h,k) is the center
we know center is (-2,-3)
h= -2, k = -3 , a= 6 and b = 4
The standard equation becomes
Foci are (h,k+c) and (h,k-c)
Plug in the a=6 and b=4
, we know h=-2 and k=-3
Foci are and
Option A is correct
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Answer:
Step-by-step explanation:
The first thing we have to do is find the measure of angle A using the fact that the csc A = 2.5.
Csc is the inverse of sin. So we could rewrite as
or more easy to work with is this:
and cross multiply to get
2.5 sinA = 1 and
which simplifies to
sin A = .4
Using the 2nd and sin keys on your calculator, you'll get that the measure of angle A is 23.58 degrees.
We can find angle B now using the Triangle Angle-Sum Theorem that says that all the angles of a triangle have to add up to equal 180. Therefore,
angle B = 180 - 23.58 - 90 so
angle B = 66.42
The area of a triangle is
where h is the height of the triangle, namely side AC; and b is the base of the triangle, namely side BC. To find first the height, use the fact that angle B, the angle across from the height, is 66.42, and the hypotenuse is 3.9. Right triangle trig applies:
and
3.9 sin(66.42) = h so
h = 3.57
Now for the base. Use the fact that angle A, the angle across from the base, measures 23.58 degrees and the hypotenuse is 3.9. Right triangle trig again:
and
3.9 sin(23.58) = b so
b = 1.56
Now we can find the area:
so
A = 2.8 cm squared