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r-ruslan [8.4K]
3 years ago
11

What is the radius of a circle whose equation is x2 y2 8x – 6y 21 = 0?

Mathematics
2 answers:
andrew11 [14]3 years ago
8 0

we know that

the standard form of the equation of the circle is

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

where

(h,k) is the center of the circle

r is the radius of the circle

In this problem we have

x^{2} +y^{2} +8x-6y+21=0

<u>Convert to standard form</u>

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

(x^{2}+8x) +(y^{2}-6y)=-21

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

(x^{2}+8x+16) +(y^{2}-6y+9)=-21+16+9

(x^{2}+8x+16) +(y^{2}-6y+9)=4

Rewrite as perfect squares

(x+4)^{2} +(y-3)^{2}=4

(x+4)^{2} +(y-3)^{2}=2^{2}

the center of the circle is (-4,3)

the radius of the circle is 2\ units

therefore

<u>the answer is</u>

the radius of the circle is 2\ units


uranmaximum [27]3 years ago
6 0

Answer:

Should be (A) on ED

Step-by-step explanation:

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Step-by-step explanation:

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Now for the last triangle we repeat the same process

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getting that the length of the sides for the last triangle is

X = 4.5*\frac{150}{100}\\ X =4.5*1.5\\X=6.75units.

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To compute the percent increase in the perimeter from the first to the fourth triangle we will use one last simple rule of three (this time the percentage will be the variable)

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.........................

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