Question

Find the equation of the parabola with vertex at the origin, focus at (3m, 0) and directrix with equation x=–3m.

Answer 1

Answer: x = (1/12m)(y^2)

Explanation:

Focus at (3m, 0)

Directrix equation, x = -3m

Distance from focus = distance from directrix

√(x-3m)^2 + (y-0)^2 = √(x - (-3m))^2 + (y -y)^2

(x - 3m)^2 + y^2 = (x + 3m)^2

y^2 = (x + 3m)^2 - (x - 3m)^2

y^2 = x^2 + 6mx + 9m^2 - x^2 +6mx - 9m^2

Collecting like terms and simplifying

y^2 = 6mx + 6mx

y^2 = 12mx

x = (1/12m)(y^2)

Answer 2

The equation of the parabola is:

`x = 12\cdot m \cdot y^(2)`

Explanation:

The equation of the parabola is:

`x = 4\cdot p \cdot y^(2)`

Where
`p` is equal to the distance between focus and vertex. Then,

`p = 3\cdot m`

Lastly, the equation of the parabola is:

`x = 12\cdot m \cdot y^(2)`