Answer to Question #219587 in Analytic Geometry for Bless

Question

Write down the Cartesian equation of a parabola with vertex at the origin and the

focus at the point (0, −2).

Answer 1

Solution.

$$(x-h)^2 = 4p(y-k)$$

where $(h,k) - vertex$, so in our case it is $(0,0)$ and distance from vertex to focus is $p$ = -2

$$(x-0)^2 = 4*(-2)*(y-0)$$

$$x^2 = -8y$$

$$y =- 1/8 * x^2$$

Answer: $y = -1/8 * x^2$