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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Which of the following is the equation of a parabola with focus (0, 2) and directrix y = -2?
x = y2/8, y = x2/8, y = x2/4, x = y2/4
Solution:
Given: Focus (0, 2) and the directrix y = -2
The equation of the parabola with focus and directrix - F(a, b) and D(y = c) is given by:
⇒ (x - a)2 + b2 - c2 = 2y(b - c)
Now substitute F(0, 2)and D(x, -2) ∀ x: y(x) = c
⇒ x2 = 2y(2- (-2))
= 2y(2 + 2))
= 8y
⇒ x2 = 8y
⇒ y = 1/8x2
The equation of parabola is y = 1/8x2.
Which of the following is the equation of a parabola with focus (0, 2) and directrix y = -2?
Summary:
y = 1/8x2 is the equation of a parabola with focus (0, 2) and directrix y = -2.
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