Question

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

Answer 1

y² + 10y + 6x + 58 = 0

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 =
`√((x+7)^2+(y+5)^2)`

Distance of the point from directrix =
`√((x+4)^2)`

Therefore, equation of the parabola will be,

`√((x+7)^2+(y+5)^2)=√((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