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Fudgin [204]
2 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]2 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

muminat2 years ago
4 0

Answer:

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

Step-by-step explanation:

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Find the expansion of cos x about the point x=0
ycow [4]

Answer:

Cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{1!} + ...

Step-by-step explanation:

We use Taylor series expansion to answer this question.

We have to find the expansion of cos x at x = 0

f(x) = cos x, f'(x) = -sin x, f''(x) = -cos x, f'''(x) = sin x, f''''(x) = cos x

Now we evaluate them at x = 0.

f(0) = 1, f'(0) = 0, f''(0) = -1, f'''(0) = 0, f''''(0) = 1

Now, by Taylor series expansion we have

f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)(x-a)^2}{2!} + \frac{f'''(a)(x-a)^3}{3!} + \frac{f''''(a)(x-a)^4}{4!} + ...

Putting a = 0 and all the values from above in the expansion, we get,

Cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{1!} + ...

8 0
3 years ago
Peyton has 10 more dollars than Bryson. If Bryson has d dollars, how much does Peyton have?
Mice21 [21]
The correct equation is d + 10
3 0
3 years ago
Read 2 more answers
Alguien puede ayudarme en esto
Montano1993 [528]
Lo siento, español no es mi primer lengua, pero trataré ayudar. ¿Qué significa L1, L2, y L3? No recuerdo.
Necesita multiplicar
x-3 • x+2
x-2 • x-1
Pero, obtendrías esto, y no ayudaría
x^2-6 = x^2+2
Es imposible resolver para x con eso.
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7 0
3 years ago
When constructing an inscribed polygon with a compass and straightedge ,how should you start the construction?
kenny6666 [7]

Place a point on your paper and then use a compass to construct a circle.

7 0
3 years ago
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area of a triangle: sine formula just please help i’m stuck and i don’t know what to do this was due yesterday
Katyanochek1 [597]

Answer:

269.0

Step-by-step explanation:

Trigonmetric area formula: 0.5 * a* b* sin(C)

a = 46

b=19

c = 38 degrees

0.5 * 46 * 19 * sin(38)

Pulg it into a calculator and you get 269.0441

Then round to the nearest tenth to get 269.0

3 0
3 years ago
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