Find the focus, directrix, and focal diameter of the parabola.
9x + 7y2 = 0
my answers were
focus = -9/28,0
fd =9/7
directrix= -9/28 (this ans. is incorrect) what am I missing? pls help
Well, what do you know ...
your problem is actually on its own webpage
http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.314229.html
To find the focus, directrix, and focal diameter of a parabola, we need to rewrite the equation in the standard form:
(x - h)^2 = 4p(y - k)
where (h, k) is the vertex and p is the distance between the vertex and the focus (or the vertex and the directrix).
In your equation, 9x + 7y^2 = 0, we can start by dividing both sides of the equation by 7 to simplify it:
x + (7/9)y^2 = 0
Now, let's complete the square to put it into the standard form.
(x + 0)^2 = -7/9(y - 0)
Comparing this to the standard form, we can see that the vertex is (h, k) = (0, 0).
The coefficient of the y-term is 1 (4p = 1), so p = 1/4.
Since p is positive, we know that the parabola opens upward.
Now we can find the focus (F) and the directrix.
The focus (F) is located at (h, k + p), so in this case, it is (0, 0 + 1/4) = (0, 1/4).
The directrix is a line parallel to the x-axis and located at a distance of p units away from the vertex. In this case, it is the line y = -1/4.
Finally, the formula for the focal diameter (fd) is given by fd = 4p. Therefore, in this case, the focal diameter is fd = 4 * (1/4) = 1.
To summarize:
Focus (F): (0, 1/4)
Directrix: y = -1/4
Focal Diameter (fd): 1
So, your answers for the focus and focal diameter are correct, but the directrix should be y = -1/4, not y = -9/28.