Answer:
y² + 10y + 6x + 58 = 0
Step-by-step explanation:
Focus of the parabola has been given as (-7, -5) and directrix as x = -4
Let a point on the parabola is (x, y).
By the definition of a parabola, "distance of a point on parabola is equidistant from focus and directrix".
Distance from focus of the given point = [tex]\sqrt{(x+7)^2+(y+5)^2}[/tex]
Distance of the point from directrix = [tex]\sqrt{(x+4)^2}[/tex]
Therefore, equation of the parabola will be,
[tex]\sqrt{(x+7)^2+(y+5)^2}=\sqrt{(x+4)^2}[/tex]
[tex](x+7)^2+(y+5)^2=(x+4)^2[/tex]
x² + 14x + 49 + y² + 10y + 25 = x² + 8x + 16
y² + 14x + 10y + 74 = 8x + 16
y² + 10y + 6x + 58 = 0