Tristabergeron5650
31.07.2019 •
Mathematics
Which is the equation of a parabola with a directrix at y = −3 and a focus at (5, 3)?
y = 1/12 (x-5)^2
y = -1/12 (x-5)^2
y = 1/12 (x+5)^2
y = -1/12 (x--+5)^2
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Ответ:
y = 1/12 (x − 5)²
Step-by-step explanation:
We can solve this graphically without doing calculations.
The y component of the focus is y = 3. Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient. That narrows the possible answers to A and C.
The x component of the focus is x = 5. Since this is above the vertex, we know the x component of the vertex is also x = 5.
So the answer is A. y = 1/12 (x−5)².
But let's say this wasn't a multiple choice question and we needed to do calculations. The equation of a parabola is:
y = 1/(4p) (x − h)² + k
where (h, k) is the vertex and p is the distance from the vertex to the focus.
The vertex is halfway between the focus and the directrix. So p is half the difference of the y components:
p = (3 − (-3)) / 2
p = 3
k, the y component of the vertex, is the average:
k = (3 + (-3)) / 2
k = 0
And h, the x component of the vertex, is the same as the focus:
h = 5
So:
y = 1/(4×3) (x − 5)² + 0
y = 1/12 (x − 5)²
Ответ:
Graph A.
Step-by-step explanation:
You want the equation in slope-intercept form, y=mx+b. In x+y=7, you want the y by itself, so subtract x on both sides to get y=-x+7. After that, on the graph, go up 7 units on the y-axis, down 1 unit indicated by -x, and 1 to the right. Strikethrough both dots and you get Graph A.