Answer to Question #255866 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.

Answer 1

We are given vertex(0,0), focus(0,-1), directrix line y=1, axis of symmetry x=0

Here (h,k)=(0,0)

Directrix: y=k-p

Focus: (h,k+p)=(0,-1)

So p=-1

The equation of the parabola is given by

(x-h)²=4p(y-k)

but h=0

Hence the equation is ;

x²=-4y