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Fudgin [204]
3 years ago
11

Write the equation for a parabola with a focus at (-7,-5) and a directrix at x = -4

Mathematics
2 answers:
Nataliya [291]3 years ago
6 0

Answer:

y² + 10y + 6x + 58 = 0

Step-by-step explanation:

Focus of the parabola has been given as (-7, -5) and directrix as x = -4

Let a point on the parabola is (x, y).

By the definition of a parabola, "distance of a point on parabola is equidistant from focus and directrix".

Distance from focus of the given point = \sqrt{(x+7)^2+(y+5)^2}

Distance of the point from directrix = \sqrt{(x+4)^2}

Therefore, equation of the parabola will be,

\sqrt{(x+7)^2+(y+5)^2}=\sqrt{(x+4)^2}

(x+7)^2+(y+5)^2=(x+4)^2

x² + 14x + 49 + y² + 10y + 25 = x² + 8x + 16

y² + 14x + 10y + 74 = 8x + 16

y² + 10y + 6x + 58 = 0

muminat3 years ago
4 0

Answer:

(y+5)^2/6 - 11/2

Step-by-step explanation:

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Given:

Sample Mean <span>= 30<span>
Sample size </span><span><span><span>= 1000</span></span><span>
</span></span></span>Population Standard deviation or <span><span><span>σ<span>=2</span></span><span>
</span></span>Confidence interval </span><span>= 95%</span>

to compute for the confidence interval

Population Mean or <span>μ<span><span>= sample mean ± (</span>z×<span>SE</span>)</span></span>

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<span><span>SE</span>→</span> Standard Error

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Critical Value of z for 95% confidence interval <span>=1.96</span>

<span>μ<span>=30±<span>(1.96×0.9486)</span></span><span>
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Upper Limit

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Lower Limit

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