Question

A parabola can be drawn given a focus of (−4,−10) and a directrix of y=−4. What can be said about the parabola?

Answer 1

A parabola can be drawn given a focus of (-4,-10) and a directrix of y=-4. The equation of the parabola is (x + 4)^2 = -72(y + 7).

Step-by-step explanation:

A parabola can be drawn given a focus of (-4,-10) and a directrix of y=-4. A parabola is a U-shaped curve that is symmetric about its vertex. The focus is a point on the parabola that is equidistant from the vertex and the directrix. The directrix is a horizontal line that is parallel to the x-axis and is a fixed distance from the vertex.

To draw the parabola, first find the vertex. The vertex can be found by calculating the average of the x-coordinate of the focus and the y-coordinate of the directrix. In this case, the vertex is (-4, -7).

Next, determine the equation of the parabola. The equation of a parabola with vertex (h, k), focus (h, k + p), and directrix y = k - p is given by (x - h)^2 = 4p(y - k). In this case, the equation of the parabola is (x + 4)^2 = -72(y + 7).

Answer 2

The answer to your question is: Yes a parabola can be drawn if we know the focus and the directrix.

Step-by-step explanation:

We can say that it is a vertical parabola that opens downwards.

We conclude that if we graph both the focus and the directrix. Also if we continue the process we can find the vertex (-4, -7) and p = 3.