# What is the equation of the parabola passing through the points (0, 0) and (0,1) and having the line x+y+1=0 as its axis of symmetry?

##### 1 Answer

Equation of parabola is

#### Explanation:

As axis of symmetry is

Further, directrix will be perpendicular to axis of symmetry and its equation would be of the form

As every point on parabola is equidistant from focus and directrix, its equation will be

This parabola passes through

Subtracting (1) from (2), we get

This reduces equation of parabola to

and as it passes through

i.e.

and hence

and equation of parabola as

or

or

or

or

graph{(x^2+y^2+2xy+5x-y)(x+y+1)(12x-12y-13)=0 [-11.42, 8.58, -2.48, 7.52]}