Answer:
[tex]y^2=-12(x+2)[/tex]
Step-by-step explanation:
The general vertex form of parabola is,
[tex](y-k)^2=a(x-h)[/tex]
where,
[tex](h.k)[/tex] is the vertex,
[tex]y=h[/tex] is the axis of symmetry.
Given the coordinates of the vertex as [tex](-2,0)[/tex] and focus as [tex](-5,0)[/tex]
a is the 4 times the distance between the vertex and the focus.
The distance between the vertex and focus is -3. Negative is because we are calculating the distance to the left (-ve x direction) of the vertex.
Hence, [tex]a=4\times(-3)=-12[/tex]
Putting the values in the general equation,
[tex](y-0)^2=-12(x-(-2))[/tex]
i.e [tex]y^2=-12(x+2)[/tex]
