Answer:
x = [tex]\frac{1}{12}[/tex] y²
Step-by-step explanation:
Any point (x, y ) on the parabola is equidistant from the focus and the directrix
Using the distance formula, then
[tex]\sqrt{(x-3)^2+(y-0)^2}[/tex] = | x + 3 |
Squaring both sides
(x - 3)² + y² = (x + 3)² ← expanding both sides
x² - 6x + 9 + y² = x² + 6x + 9 ← subtract x² + 6x + 9 from both sides
- 12x + y² = 0 ( subtract y² from both sides )
- 12x = - y² ( divide both sides by - 12 )
x = [tex]\frac{1}{12}[/tex] y²
Answer:
y²-12x = 0
Step-by-step explanation:
The formula for calculating the equation of a parabola is y² = 4ax
and x = a
To find the equation of the parabola with focus (3, 0) and directrix x = –3,
The point given (x,y) = (3,0) and x = -3
From the data given, it can be seen that a = -3 by simply comparing x = a with x = -3
Similarly, x = 3 from the given point.
Substituting the value of x = -3 in the formula for equation of a parabola gives;
y² = 4(-3)x
y²= -12x
y²-12x = 0
