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vladimir1956 [14]
3 years ago
7

The general form of the equation of a circle is x2 + y2 + 8x + 22y + 37 = 0.

Mathematics
2 answers:
alexandr1967 [171]3 years ago
8 0

we know that

the equation of the circle in standard form is equal to

(x-h)^{2}+(y-k)^{2}=r^{2}

where

(h,k) is the center of the circle

r is the radius of the circle

we have

x^{2}+y^{2} +8x+22y+37=0

Convert to standard form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(x^{2}+8x)+(y^{2} +22y)=-37

Complete the square twice. Remember to balance the equation by adding the same constants to each side

(x^{2}+8x+4^{2})+(y^{2} +22y+11^{2})=-37+4^{2}+11^{2}

(x^{2}+8x+16)+(y^{2} +22y+121)=-37+16+121

(x^{2}+8x+16)+(y^{2} +22y+121)=100

Rewrite as perfect squares

(x+4)^{2}+(y+11)^{2}=10^{2}

the  center is the point (-4,-11)

the radius is r=10\ units

therefore

<u>The answer is</u>

a) the equation in standard form is (x+4)^{2}+(y+11)^{2}=10^{2}

b) the  center of the circle is the point (-4,-11) and the radius of the circle is r=10\ units

see the attached figure to better understand the problem

Fudgin [204]3 years ago
7 0
Hello,

x²+y²+8x+22y+37=0
==>(x²+2*4x+16)+(y²+2*11y+121)+37-16-121=0
==>(x+4)²+(y+1)²=10²
Center=(-4,-1) , radius=10
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Answer:

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85 \le \frac{75 + 97 + n}{3} \le 90

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85 \le \frac{75 + 97 + n}{3}

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Multiply both sides by 3

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172 + n \le 270

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