What is the circumference of the circle defined by x^2+6x +y^2-12y-4=0.

Mathematics

1 answer:

KengaRu [80]3 years ago

5 0

Answer:

44.0

Step-by-step explanation:

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Find the length of the segment.<br><br> please help

maksim [4K]

Answer:

$\sqrt{29}$

Step-by-step explanation:

Use the distance formula!

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

If we plug in the coordinates:

$d=\sqrt{(3-(-2))^2+(4-2)^2} \\d=\sqrt{25+4}\\ d=\sqrt{29}$

That's our answer!

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2 years ago

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the temperature 0 F ,3 F ,6 F ,5 F,and -1 F have also been recorded in florida .graph these temperature on the number line .

Brut [27]

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3 years ago

Which equation represents the equation of the parabola with focus (-3 3) and directrix y=7?

Artemon [7]

Answer:

The equation $y=\frac{-x^2-6x+31}{8}$ represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula $d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$ , we find that the distance between (x, y) is

$\sqrt{(x+3)^2+(y-3)^2}$

and the distance between (x, y) and the directrix y = 7 is

$\sqrt{(y-7)^2}$ .

On the parabola, these distances are equal so, we solve for y:

$\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}$