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Solution 4.1:5b

From Förberedande kurs i matematik 1

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If the circle is to contain the point (-1,1), then that point's distance away from the centre (2,-1) must equal the circle's radius, r. Thus, we can obtain the circle's radius by calculating the distance between (-1,1) and (2,-1) using the distance formula,

r=(2−(−1))2+(−1−1)2=32+(−2)2=9+4=13. 

When we know the circle's centre and its radius, we can write the equation of the circle,

(x−2)2+(y−(−1))2=(13)2 

which the same as

(x−2)2+(y+1)2=13.



Note: A circle having its centre at (a,b) and radius r has the equation

(x−a)2+(y−b)2=r2.
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