Question

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

Answer 1

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