Allison and Amy Scott work 15 hours per week at separate jobs. Allison assists in a hospital for $5.25 per hour. Amy works in a
2 answers:
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Answer:
a)
b)
c)
Step-by-step explanation:
Start by isolating the trigonometric expression in both equations, ad then use the Pythagorean identity:
to obtain the standard equation of a conic.
then:
this is the equation of an ellipse centered at (h,k), and with horizontal axis length = 2a , and vertical axis length = 2b.
The parametric equations are those we started with:
but we need to find the appropriate parameters for the requested ellipse, as shown below.
For an ellipse of vertices (-4,0) a,d (6,0) and foci at (-2,0) and (4.0), we are dealing with an ellipse with major horizontal axis on the line y=0, and major diameter length of 10 units, so the parameter . The center of the ellipse is therefore at (1,0).
We recall that the vertices of a translated horizontal ellipse are located at and
, then k=0 to satisfy the information given (-4,0) & (6,0), and since
, we deduce that
and therefore h=1.
To find "b" (the only parameter missing for the standard equation of the conic), we need the information on the foci (-2,0) and (4,0) which must equal (h-c,k) and (h+c,k) with k=0 and h=1 which then gives that c=3
Now using the formula for the parameter "c" of the foci:
Then we can write the equation of this ellipse in standard form as: