Answer:
The equation of parabola: [tex]y=\dfrac{1}{4}(x+5)^2-2[/tex]
Step-by-step explanation:
The focus of a parabola is (−5,−1) and the directrix is y=−3
Focus and Directrix are equi-distance from vertex.
Directrix: y=-3 and Focus: (−5,−1)
Thus, The Vertex: (−5,−2)
Equation of parabola: [tex]y=a(x-h)^2+k[/tex]
Distance between Focus and Vertex (p) = 1
[tex]a= \frac{1}{4p}=\frac{1}{4}[/tex]
Substitute vertex and value of a into formula
Hence, The equation of parabola: [tex]y=\dfrac{1}{4}(x+5)^2-2[/tex]
