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3 years ago

15 points!

Mathematics

1 answer:

lord [1]3 years ago

4 0

Answer:

(x+5)² + (y+6)² = 9

Step-by-step explanation:

the equation of a circle is

(x-a)² + (y-b)² = r²

with (a,b) being the center coordinates and r being the radius (half the diameter).

so, in our case here a = -5, b = -6

and r is the distance from the center to any point of the circle. that includes the lowest point asking the edge.

the distance of (-5,-6) to (-5,-9) is 3, as both points have the same x-value, and the only difference is in the y-value.

as we are talking about a distance, negative values don't make sense. so, we need the absolute value of -9 - -6 or then of -3, and that is 3.

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We have a separable equation, first let's rewrite the equation as:

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$\int\ \frac{dy}{3a+y} =\int\cot(x) \, dx$

Evaluating the integrals:

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Where C1 is an arbitrary constant.

Solving for y:

$y(x)=-3a+e^{C_1} sin(x)$

$e^{C_1} =constant$

So:

$y(x)=C_1*sin(x)-3a$

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$y(\frac{\pi}{3} )=3a=C_1*sin(\frac{\pi}{3})-3a\\ 3a=C_1*\frac{\sqrt{3} }{2} -3a$

Solving for C1:

$C_1=4a\sqrt{3}$

Therefore:

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4 years ago