3. Write the equation of a parabola with focus (-2, 4) and directrix y = 2. Show your work, including a sketch.
1 answer:
To solve this problem you must apply the proccedure shown below:
1. (x0,y0) is any point of the parabola.
2. You have that the distance between (x0,y0) and the the focus (-2,4) is:
√(x0-(-2))²+(y0-4))²
√((x0-+2)²+(y0-4))²
3. The distance between (x0,y0) and the directrix y=2, is:
|y0-2|
4. Then, you have:
√((x0-+2)²+(y0-4))²= |y0-2|
5. When you simplify it and you clear y0, you obtain:
y0=(x0²/4)+x0+4
6. Therefore, <span>the equation of the parabola with focus (-2, 4) and directrix y = 2, is:
</span>
y=(x²/4)+x+4
7. The graph is shown in the figure attached.
The answer is: y=(x²/4)+x+4
1. (x0,y0) is any point of the parabola.
2. You have that the distance between (x0,y0) and the the focus (-2,4) is:
√(x0-(-2))²+(y0-4))²
√((x0-+2)²+(y0-4))²
3. The distance between (x0,y0) and the directrix y=2, is:
|y0-2|
4. Then, you have:
√((x0-+2)²+(y0-4))²= |y0-2|
5. When you simplify it and you clear y0, you obtain:
y0=(x0²/4)+x0+4
6. Therefore, <span>the equation of the parabola with focus (-2, 4) and directrix y = 2, is:
</span>
y=(x²/4)+x+4
7. The graph is shown in the figure attached.
The answer is: y=(x²/4)+x+4
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Answer:
Evening walk is shorter.
Step-by-step explanation:
We have been given that a nature center offers 2 guided walks. The morning walk is two-third mile. The evening walk is three-sixths mile. We are asked to find the shorter walk.
Let us compare both fractions by making the same denominator.
Upon making common denominator, we can see that two-thirds are equal to four sixths.
Since three-sixths is less than four-sixths, therefore, evening walk is shorter.
We will draw two rectangles, one with 6 sub-parts and other with three sub-parts.
We will shade 2 parts out of 3 sub-parts to represent 2/3 and shade 3 parts out of 6 sub-parts to represent 3/6.
Then we will further divide three sub-parts into 6 sub-parts as shown in the diagram that will represent 4/6.
