What is the equation of a parabola that has a focus at (0, −3) and a directrix,y = 3 ?
2 answers:
Refer to the diagram shown.
At an arbitrary point P (x,y) on the parabola, the distance from the focus should be equal to the distance from the directrix.
The distance of P from the focus is
d₁ = √[x² + (y+3)²]
The distance from P to the directrix is
d₂ = 3 - y
Therefore
d₁ = d₂.
That is,
x² + (y+3)² = (3 - y)²
x² + y² + 6y + 9 = 9 - 6y + y²
x² + 12y = 0
y = - (1/12) x²
Answer:
At an arbitrary point P (x,y) on the parabola, the distance from the focus should be equal to the distance from the directrix.
The distance of P from the focus is
d₁ = √[x² + (y+3)²]
The distance from P to the directrix is
d₂ = 3 - y
Therefore
d₁ = d₂.
That is,
x² + (y+3)² = (3 - y)²
x² + y² + 6y + 9 = 9 - 6y + y²
x² + 12y = 0
y = - (1/12) x²
Answer:
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The given equation is :
1. The relationship such that dependent variable (y) is isolated is :
2. The table accompanying this equation :
- x = -4 and y = 0.5
- x = -1 and y = 2
- x = - 0.5 and y = 4
- x = 0 and y = undefined
- x = 0.5 and y = -4
- x = 1 and y = -2
- x = 4 and y = -0.5
3. graph of the given equation is in attachment ~
