MATH SOLVE

2 months ago

Q:
# 3. Write the equation of a parabola with focus (-2, 4) and directrix y = 2. Show your work, including a sketch.

Accepted Solution

A:

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, the equation of the parabola with focus (-2, 4) and directrix y = 2, is:

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, the equation of the parabola with focus (-2, 4) and directrix y = 2, is:

y=(x²/4)+x+4

7. The graph is shown in the figure attached.

The answer is: y=(x²/4)+x+4