Problems from Equation of the vertical parabola with generic vertex

Pick a point on the plane. Find the equation of the vertical parabola whose focus is the chosen point and has $p = 14$ .

See development and solution

Development:

Choosing $F (5, 5)$ and identifying with $F (x_{0}, y_{0} + \frac{p}{2})$ we have $x_{0} = 5$ and $y_{0} + \frac{p}{2} = 5$ . We can also compute $y_{0} = 5 - \frac{14}{2} = 5 - 7 = - 2$ .

We have the necessary elements of the equation. Substituting in $(x - x_{0})^{2} = 2 p (y - y_{0})$ we obtain $(x - 5)^{2} = 28 (y + 2)$

Solution:

Taking the point $F (5, 5)$ we obtain the parabola $(x - 5)^{2} = 28 (y + 2)$ .

Hide solution and development