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Fudgin [204]
2 years ago
11

Write the equation for a parabola with a focus at (-7,-5) and a directrix at x = -4

Mathematics
2 answers:
Nataliya [291]2 years ago
6 0

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 = \sqrt{(x+7)^2+(y+5)^2}

Distance of the point from directrix = \sqrt{(x+4)^2}

Therefore, equation of the parabola will be,

\sqrt{(x+7)^2+(y+5)^2}=\sqrt{(x+4)^2}

(x+7)^2+(y+5)^2=(x+4)^2

x² + 14x + 49 + y² + 10y + 25 = x² + 8x + 16

y² + 14x + 10y + 74 = 8x + 16

y² + 10y + 6x + 58 = 0

muminat2 years ago
4 0

Answer:

(y+5)^2/6 - 11/2

Step-by-step explanation:

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