Find the equation of parabola that satisfies the given condition
Vertex (0,0), focus (-2,0)

Explanation

Here, vertex `O-=(0,0), "focus" S -=(-2,0)`
`:.` OS=2
`rArr` Distance of directrix from vertex = 2
Now, equation of directrix x=2
`rArr` x-2=0
Let P (x,y) be a varibale point on the parabola.
Now, distance of P from focus S
=perpendicular distance from P to the directrix
`rArrsqrt((x+2)^(2)+(y-0)^(2))=x-2`
`rArr(x+2)^(2)+y^(2)=(x-2)^(2)`
`rArr" "y^(2)=-8x`