Find the standard form of the equation of the parabola with a focus at (-8, 0) and a directrix at x = 8

1 answer:

8 0

The best thing to do when finding conic equations from the focus and directrix is to sketch a little graph. When you do this, you can easily identify the vertex right in the middle and can determine if the parabola is vertical or horizontal since it must wrap around the focus. This way you know whether the x or the y is squared. When you sketch the focus and directrix, you will see the vertex is at (0,0) and the parabola is sideways, so the y is squared. now remember your formula is y^2=4px where p is the distance from the vertex to the focus, or you could write x=1/(4p)y^2. Now from 0 to -8 is -8 so that means 4p=-32. This gives you y^2=-32x or x=-1/32y^2. Thsi type of question will also be on your module exam and then the final exam so be sure to practice some:)

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Answer:

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Step-by-step explanation:

because a hyper bole is (y-k) 2b2 -(x-h) 2a2=1

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Mrac [35]

This makes a right triangle with hypotenuse x+2 and legs 10 and x

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Galina-37 [17]

Answer:

At first find the lowest common multiple of 3, 4, 10

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3 years ago

Solve the system by substitution.<br> - 8x + y = -32<br> - 3x – 10 = y<br> (,)

agasfer [191]

Answer:

$x=2,\:y=-16$

Step-by-step explanation:

$\begin{bmatrix}-8x+y=-32\\ -3x-10=y\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:-8x+y=-32:\quad x=-\frac{-32-y}{8}\\\\\mathrm{Subsititute\:}x=-\frac{-32-y}{8}\\\begin{bmatrix}-3\left(-\frac{-32-y}{8}\right)-10=y\end{bmatrix}\\\\Simplify\\\begin{bmatrix}\frac{3\left(-32-y\right)}{8}-10=y\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:\frac{3\left(-32-y\right)}{8}-10=y:\quad y=-16\\\\\mathrm{For\:}x=-\frac{-32-y}{8}\\\\\mathrm{Subsititute\:}y=-16\\x=-\frac{-32-\left(-16\right)}{8}\\$

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Knitting: You are knitting a blanket. You want the area of the blanket to be 24ft^2. You want the length of the blanket to be 2

andriy [413]

You can use factors to solve. Determine all the factor pairs of 24, find the two that are two numbers apart.
1, 24 X
2, 12 X
3, 8 X
4, 6 YES!

Algebraic way to solve using Quadratics:
l = 2 + w

A = lw

A = (2 + w)w Substitute (2 + w) for l

24 = (2 + w)w Substitute 24 in for the area

24 = 2w + w^2 Distribute

w^2 + 2w - 24 = 0 Set equal to 0 (put in standard form)

(w + 6) (w - 4) = 0 Factor

w + 6 = 0 and w - 4 = 0 Set each factor equal to 0.

So w= -6 or w = 4 ... -6 makes no sense for a length! So the width must be 4 and the length will be 4 + 2, which is 6.

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