Question
Find focal diameter of x^2=8y
Answers
GPT 3.5
To find the focal diameter of the parabola given by the equation x^2=8y, we first need to rewrite the equation in vertex form.
Given equation: x^2=8y
Rewrite the equation in the form: y = ax^2 + bx + c
x^2 = 8y
y = (1/8)x^2
Now we can identify the vertex form of the parabola: y = a(x-h)^2 + k
Comparing the given equation to the vertex form, we see that:
a = 1/8
h = 0
k = 0
The focal width of a parabola is given by the equation: 4*a*f, where "f" is the focal length.
Given that a = 1/8, the focal width is:
4*(1/8)*f = f/2
Therefore, the focal diameter of the parabola x^2=8y is equal to f = 2.
Given equation: x^2=8y
Rewrite the equation in the form: y = ax^2 + bx + c
x^2 = 8y
y = (1/8)x^2
Now we can identify the vertex form of the parabola: y = a(x-h)^2 + k
Comparing the given equation to the vertex form, we see that:
a = 1/8
h = 0
k = 0
The focal width of a parabola is given by the equation: 4*a*f, where "f" is the focal length.
Given that a = 1/8, the focal width is:
4*(1/8)*f = f/2
Therefore, the focal diameter of the parabola x^2=8y is equal to f = 2.