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26.08.2020 •
Mathematics
Write an equation in standard form for each of the following conic sections.
a. A parabola with vertex (1, 2) and directrix y = -2
b. A circle with center (2, 3) passing through the point (-3, 5)
c. A parabola with focus (-1,0) and directrix x = 1.
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Ответ:
Table #1:
Using the first two points (2,1) and (5,3)
You get (x-2)/3 = (y-1)/2
But then the 3rd point (8,7) does not work, so this is not linear.
Table #2
Using the first two points (1,10) and (2,13)
You get x-1 = (y-10) /3
But then the 3rd point (3,18) does not work so this is also not linear.
Table #3
Using the first two points (2,1) and (4,6)
You get x-2 /2 = y-1 /5
And all the other points will work with this, which makes this table linear.
Rewrite the equation to get y = 5/2x-4