Solved: "What is the radius length of the circle..."

High School
Geometry
High school geometry
Circles

Armorikam

Answered question

2021-06-30

What is the radius length of the circle with equation

x^{2} + y^{2} - x + y - 4 = 0

Answer & Explanation

Dora

Skilled2021-07-01Added 98 answers

The standard equation of a circle with center (h,k) and radius rr is given by: ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$
So, we write the given in this form.
Isolate the constant and group the x’s and y’s:
$(x^{2} - x) + (y^{2} + y) = 4$
Complete the square:
$((x^{2}) - x + {(\frac{1}{2})}^{2}) + ((y^{2} + y + 1 {(\frac{1}{2})}^{2}) = 4 + {(\frac{1}{2})}^{2} + {(\frac{1}{2})}^{2}$
$(x - (\frac{1}{2})) + {(y + (\frac{1}{2}))}^{2} = 4 + \frac{1}{4} + \frac{1}{4}$
${(x - (\frac{1}{2}))}^{2} + {(y + \frac{1}{2})}^{2} = \frac{18}{4}$
Hence, we can solve for the radius rr by writing: $r^{2} = \frac{18}{4}$
$r = \frac{\sqrt{18}}{2}$
$r = 3 \frac{\sqrt{2}}{2}$

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