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Mnenie [13.5K]
3 years ago
9

What is the radius of a circle with the equation x^2+y^2+6x-2y+3?

Mathematics
2 answers:
atroni [7]3 years ago
8 0

Answer:

r = √13

Step-by-step explanation:

Starting with x^2+y^2+6x-2y+3, group like terms, first x terms and then y terms:  x^2 + 6x            + y^2 -2y             = 3.  Please note that there has to be an " = " sign in this equation, and that I have taken the liberty of replacing " +3" with " = 3 ."  

We need to "complete the square" of x^2 + 6x.  I'll just jump in and do it:  Take half of the coefficient of the x term and square it; add, and then subtract, this square from x^2 + 6x:     x^2 + 6x  + 3^2 - 3^2.  Then do the same for y^2 - 2y:  y^2 - 2y + 1^2 - 1^2.

Now re-write the perfect square x^2 + 6x + 9 by (x + 3)^2.  Then we have x^2 + 6x + 9 - 9; also y^2 - 1y + 1 - 1.  Making these replacements:

(x + 3)^2 - 9 + (y - 1)^2 -1 = 3.  Move the constants -9 and -1 to the other side of the equation:  (x + 3)^2 + (y - 1)^2 = 3 + 9 + 1 = 13

Then the original equation now looks like (x + 3)^2 + (y - 1)^2 = 13, and this 13 is the square of the radius, r:  r^2 = 13, so that the radius is r = √13.


Komok [63]3 years ago
5 0

Answer:

2.646

Step-by-step explanation:

Complete the square, put the equation in standard form, then evaluate the radius.

... x² + y² + 6x - 2y +3 = 0 . . . . given equation in general form

... x² +6x + 9 +y² -2y +1 = -3 +9 +1 . . . . add the squares of half the coefficients of the x- and y-terms; subtract 3

... (x +3)² +(y -1)² = 7 . . . . standard form equation for a circle

The term on the right, 7, is the square of the radius. so the radius is ...

... r = √7 ≈ 2.646

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Option C) a_{n}=m-b+m(n-1) for n={\{1,2,3,...}\} is not the correct way to define the given infinite sequence

{\{m+b,2m+b,3m+b,4m+b,...}\}

Step-by-step explanation:

Given infinite sequence is {\{m+b,2m+b,3m+b,4m+b,...}\}

Option B) a_{n}=m-b+m(n-1) for n={\{1,2,3,...}\} is not the correct way to define the given infinite sequence {\{m+b,2m+b,3m+b,4m+b,...}\}

Now verify  a_{n}=m-b+m(n-1) for n={\{1,2,3,...}\} is true for the given infinite sequence

That is put n=1,2,3,.. in the above function

a_{n}=m-b+m(n-1)

When n=1,  a_{1}=m-b+m(1-1)

=m-b+0

a_{1}=m-b\neq m+b

When n=2,  a_{2}=m-b+m(2-1)

=m-b+m

a_{2}=2m-b\neq 2m+b

When n=3,  a_{3}=m-b+m(3-1)

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a_{3}=3m-b\neq 3m+b

and so on.

Therfore a_{n}=m-b+m(n-1) for n={\{1,2,3,...}\} is not the correct way to define the given infinite sequence

{\{m+b,2m+b,3m+b,4m+b,...}\}

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