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morpeh [17]
3 years ago
14

X^2 + Y^2 +ax + 2y + 3 = 0 What number is this equation the equation of a circle?

Mathematics
1 answer:
Sav [38]3 years ago
6 0

Answer:

Eq: (x+a/2)²+(y+1)²=(a²-8)/4

Center: O(-a/2, -1)

Radius: r=0.5×sqrt(a²-8)

Mandatory: a>2×sqrt(2)

Step-by-step explanation:

The circle with center in O(xo,yo) and radius r has the equation:

(x-xo)²+(y-yo)²=r²

We have:

x²+y²+ax+2y+3=0

But: x²+ax=x²+2(a/2)x+a²/4-a²/4= (x+a/2)²-a²/4

And

y²+2y+3=y²+2y+1+2=(y+1)²+2

Replacing, we get:

(x+a/2)²-a²/4+(y+1)²+2=0

(x+a/2)²+(y+1)²=a²/4-2=(a²-8)/4

By visual inspection we note that:

- center of circle: O(-a/2, -1)

- radius: r=sqrt((a²-8)/4)=0.5×sqrt(a²-8). This means a²>8 or a>2×sqrt(2)

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The exact measure of the angle is 45°.

<h3>How to get the angle?</h3>

We know that the terminal side passes through a point of the form (√2/2, y).

Notice that the point is on the unit circle, so its module must be equal to 1, so we can write:

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We know that y is positive because the point is on the first quadrant.

Now, we know that our point is:

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And we can rewrite:

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Finally, remember that a point (x, y), the angle that represents it is given by:

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If you want to learn more about angles, you can read:

brainly.com/question/17972372

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2 years ago
If f(x) =7 +4x and g(x) =1/2 what is the value of (f/g)
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