Question

Find the equation of a parabola having the vertex at (0,1) and the focus at(0,0).

Answer 1

Answer:

The equation of the required parabola is

$\bf\,(y-1)^2=-4x$

Step-by-step explanation:

Since focus (0,0) lies left to the vertex (0,1), the parabola is open leftward

$\text{The equation of the parabola is }\bf\;(y-k)^2=-4a(x-h)$

$\text{Here,(h,k)=(0,1)}$

$\text{Also, a=distance between focus and vertex}$

$\implies\bf\,a=1$

$\text{The equation of the required parabola is }$

$(y-1)^2=-4(1)(x-0)$

$\implies\boxed{\bf\,(y-1)^2=-4x}$