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3 years ago

Find the standard form of the equation of the parabola with a focus at (-7, 0) and a directrix at x = 7.

Mathematics

2 answers:

Volgvan3 years ago

8 0

x = 1/(4p)*y^2

x = 1/(4*-7)*y^2

x = -1/28*y^2

34kurt3 years ago

5 0

Answer:

y^2 = -28x.

Step-by-step explanation:

The general form for this type of parabola is y^2 = 4ax where the focus is at (a,0) and the directrix is x = -a.

So substituting we get

y^2 = 4 * -7 * x

y^2 = -28x

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Step-by-step explanation:

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3 years ago

Determine which ordered pairs are solutions to the equation 3x+7y=21

mafiozo [28]

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(0,3) and (7,0) are solutions.

Step-by-step explanation:

In a pair of coordinates, they are always listed as (x,y). Since this is the case, you plug in each coordinate to their respective places.

For (0,3)

3(0) + 7(3) = 21

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4 years ago

Write the equation of the line that passes through the given point and is parallel to the given line.

romanna [79]

(Note: this answer is assuming that the equation has to be put in slope-intercept format.)

Answer:

$y = \frac{1}{2} x - \frac{5}{2}$

Step-by-step explanation:

1) Let's use the point-slope formula to determine what the answer would be. To do that though, we would need two things: the slope and a point that the equation would cross through. We already have the point it would cross through, (-3,-4), based on the given information. So, in the next step, let's find the slope.

2) We know that the slope has to be parallel to the given line, $y = \frac{1}{2}x - 8$ . Remember that slopes that are parallel have the same slope - so, let's simply take the slope from the given equation. Since it's already in slope-intercept form, we know that the slope then must be $\frac{1}{2}$ .

3) Finally, let's put the slope we found and the x and y values from (-3, -4) into the point-slope formula and solve:

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Therefore, $y = \frac{1}{2}x - \frac{5}{2}$ is our answer. If you have any questions, please do not hesitate to ask!

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3 years ago