Problem

Find the vertex, focus, and directrix of the para…

03:06

Problem 4 Easy Difficulty

Find the vertex, focus, and directrix of the parabola and sketch its graph.

$ 3x^2 + 8y = 0 $

Answer

$$
\begin{array}{l}{\text { Vertex is }(0,0)} \\ {\text { Focus is }\left(0,-\frac{2}{3}\right)} \\ {\text { Directrix is } y=\frac{2}{3}}\end{array}
$$

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Calculus 2 / BC

Calculus

Chapter 10

Parametric Equations and Polar Coordinates

Section 5

Conic Sections

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Video Transcript

So we have the following equation and we want Thio find all the pieces of the proble and schedule. So first we just settle for other X squared r Y squared to get it to look like one of the standard for mills. So since we have X squared in our equation, that's all for that. So first we subtract a part of the other side and then divide by the three so we get X squared is equal to negative 8/3. Why, Um, so since we have on X squared, we know it's gonna be either open up or open down since our coefficients negative. That tells me that our problem is gonna be opening toe onward. Ah, so now this looks like Formula One in the book. Um, so we're gonna compare it to X squared equals four p. Why? So that tells me that four p has to be equal to negative eight or three. So now I can solve for P by dividing both sides by four, which is the same is multiplying by 1/4. So this tells us that P is equal to minus two over. So, um, the equation for this proble here has Vertex zero since we're not subtracting anything, um, from the X and A Y, the focus is located at zero comma p, which in our case, is zero negative 2/3. And the direct tricks remember is a line. And for this equation that's located at why equals negative p um, which in this case for us is negative negative 2/3. So becomes a positive 2/3. So now, um, we're in good shape to draw sketch. So first we know over Texas as 00 the focus is at zero negative. 2/3 on the direct tricks is that why equals 2/3 So that's gonna be a horse on a line through 2/3 on the Y axis. And we know that the Vertex, um, are sorry. The problem always opens away from the direct tricks and contains the focus inside me. So this is a sketch of our craft

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