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altavistard
Hint:  Make your "x2 + y2 – x + 10y + 13 = 0" clearer by using " ^ " to indicate exponentiation:

x^2 + y^2 – x + 10y + 13 = 0

Rearrange this so that x terms are together and y terms are also (separately):

x^2  - 1x + y^2 + 10y + 13 = 0

Complete the square twice:  once for x and once for y:

(x^2 - 1x + (-1/2)^2 - (-1/2)^2 + y^2 + 10y + 25 - 25 = - 13

  Condense:

    (x-1/2)^2 + (y+5)^2  - 1/4 - 25 = -13

Combine -1/4, -25 and -13:

   (x-1/2)^2 + (y+5)^2  - 1/4 - 25 = -13 + 1/4 + 25  =  11 3/4 = 47/4

Then we have    (x-1/2)^2 + (y+5)^2  =  47/4, and r^2 = 47/4.  Then the radius of the circle is sqrt(47/4) = sqrt(47)/2  (answer)
ashishdwivedilVT

The given equation of circle had radius 3.5 units.

What is Circle?

A circle is a round 2-dimensional shape. It is a closed shape with a distance from center to circumference termed as radius 'r' and distance from one point on the circumference to another point passing through center termed as diameter 'd'.

Here, given equation of circle;

x² + y² - x + 10y + 13 = 0

Now, applying completing the square method;

x² - x + y² + 10y + 13 = 0

x² - 2 X 1/2 X x + (1/2)² - (1/2)² + y² + 2X5Xy + 5² - 5² + 13 = 0

(x - 1/2)² - 1/4 + (y + 5)² - 25 + 13 = 0

(x - 1/2)² + (y + 5)² = 1/4 + 25 - 13

(x - 1/2)² + (y + 5)² = 1/4 + 12

(x - 1/2)² + (y + 5)² = 49/4

(x - 1/2)² + (y + 5)² = (7/2)²        ...............(i)

Now, general equation of circle;

(x - a)² + (y - b)² = r²

On comparing general equation with equation 1, we get

r = 7/2

r = 3.5 units.

Thus, the given equation of circle had radius 3.5 units.

Learn more about Circle from:

https://brainly.com/question/17357009

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