Question

use the distance formula to write an equation of the parabola with vertex (0,0) and focus (0, - 10). an equation of the parabola is y = □

Explanation:

Step1: Find the value of \(p\)

The vertex is \((h,k)=(0,0)\) and the focus is \((h,k + p)=(0,-10)\). So, \(k + p=-10\), since \(k = 0\), then \(p=-10\).

Step2: Use the standard form of the parabola equation

The standard form of a parabola with vertical axis is \((x - h)^2=4p(y - k)\). Substitute \(h = 0\), \(k = 0\), \(p=-10\) into the equation: \((x-0)^2=4\times(-10)(y - 0)\).

Step3: Simplify the equation

\(x^{2}=-40y\), then \(y=-\frac{1}{40}x^{2}\).

Answer:

\(-\frac{1}{40}x^{2}\)