Answer to Question #255847 in Analytic Geometry for Baldimaruta

Question

Write the standard form of equation of parabola given the following properties: vertex (0,0); focus (0,-1); directrix line y=1; and axis of symmetry x=0. (use ^2 for "squared";

Answer 1

Let us write the standard form of equation of parabola given the following properties: vertex $(0,0);$ focus $(0,-1);$ directrix line $y=1;$ and axis of symmetry $x=0.$

The standard form of equation of parabola vertex $(0,0),$ focus $(0,-c),$ directrix line $y=c$ and axis of symmetry $x=0$ is of the form $x^2=-4cy.$ It follows that $c=1,$ and consequently the standard form of equation of parabola is $x^2=-4y.$