Question

describe the key features of a parabola with the equation $x^2 = 40y$. the value of $p$ is 10. the parabola opens up. the coordinates of the focus are $(0,10)$. the equation for the directrix is. $x = -10$ $x = 10$ $y = -10$ $y = 10$

Explanation:

Step1: Recall parabola standard form

For a parabola with equation \(x^2 = 4py\), the directrix is \(y=-p\).

Step2: Identify \(p\) from given equation

Given \(x^2 = 40y\), compare with \(x^2 = 4py\). So \(4p = 40\), which gives \(p = 10\).

Step3: Find directrix equation

Using the formula for directrix \(y=-p\), substitute \(p = 10\). So directrix is \(y=-10\).

Answer:

\(y = -10\)