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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