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zmey [24]
3 years ago
8

Derive the equation of the parabola with the focus is (-7,5) and the directrix of y=-11

Mathematics
1 answer:
Volgvan3 years ago
8 0
So, notice, the focus point is at -7, 5, and the directrix is at y = -11.

keep in mind that the vertex is half-way between those two fellows, and the distance from the vertex to either one of them is "p" units, check the picture below.

with that focus point and that directrix, the half-way over the axis of symmetry will be -7, -3, that's where the vertex is at, and notice the distance "p", is 8 units.

since the parabola is opening upwards, "p" is positive 8.

\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
4p(x- h)=(y- k)^2
\\\\
\boxed{4p(y- k)=(x- h)^2}
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ( h, k)\\\\
 p=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
h=-7\\
k=-3\\
p=8
\end{cases}\implies 4(8)[y-(-3)]=[x-(-7)]^2
\\\\\\
32(y+3)=(x+7)^2\implies y+3=\cfrac{1}{32}(x+7)^2
\\\\\\
y=\cfrac{1}{32}(x+7)^2-3

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Step-by-step explanation:

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Write the expression as a square of a monomial. <br><br><br><br><br><br><br><br><br><br> a 81x^4
poizon [28]

Answer:

(9x²)²

Step-by-step explanation:

Given the expression 81x⁴, to write the expression as a square of a monomial, first we will assign a variable to the expression.

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Then we take the square root of both sides of the expression

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Squaring both sides of the resulting equation to get y back

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What are the ordered pairs of thesolutions for this system of equations? f(x) = x^2 – 2x + 3; f(x) = -6x
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First you subtract the two equations

x^2-2x+3-6x

You simplify that and get

x^2+4x+3 = 0

Now we solve using the quadratic formula.

We get x = -1 and x = -3.

Now we find the y values by plugging the x values into the equation.

f(x) is the same as y.

y = (-1)^2 - 2(-1) + 3

y = 1+2+3

y = 6

Now for the other x value.

y = (-3)^2 - 2(-3) + 3

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So the two ordered pairs are (-1,6) and (-3,18)

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2 years ago
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Step-by-step explanation:

3/4(14x+8)-(1/2x+2)=3/8(4-x)-1/4

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37/4=-17x

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-37/68=x

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