Write the equation for a parabola with the focus at

2 answers:

5 0

The answer is (y - 4)2 = -12(x - 2)
Since the graph is facing the left, the starting equation would be (y - k)2 = -4p(x - h).
(h, k) is the vertex of the graph. If you plot the focus and the directrix, you can see that the distance is 6. Divide 6 by 2, thus the vertex should be 3 squares away from the focus and 3 squares away from the directrix. The vertex is (2, 4). And since the distance from the focus to the vertex and the distance from the directrix to the vertex is 3, P = 3.
Insert the numbers in and you should get the last choice.

Flura [38]3 years ago

3 0

Answer:

Step-by-step explanation:

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Find the Y-coordinate of point P that lies 1/3 along segment RS, where R (-7, -2) and S (2, 4).

QveST [7]

Solution:

Given that the point P lies 1/3 along the segment RS as shown below:

To find the y coordinate of the point P, since the point P lies on 1/3 along the segment RS, we have

$\begin{gathered} RP:PS \\ \Rightarrow\frac{1}{3}:\frac{2}{3} \\ thus,\text{ we have} \\ 1:2 \end{gathered}$

Using the section formula expressed as

$[\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}]$

In this case,

$\begin{gathered} m=1 \\ n=2 \end{gathered}$

where

$\begin{gathered} x_1=-7 \\ y_1=-2 \\ x_2=2 \\ y_2=4 \end{gathered}$

Thus, by substitution, we have

$\begin{gathered} [\frac{1(2)+2(-7)}{1+2},\frac{1(4)+2(-2)}{1+2}] \\ \Rightarrow[\frac{2-14}{3},\frac{4-4}{3}] \\ =[-4,\text{ 0\rbrack} \end{gathered}$

Hence, the y-coordinate of the point P is