The given equation of circle is x2+y2–14x–16y+88=0 . Let us rewrite it in a form (x−x0)2+(y−y0)2=R2,(1)
where x0 and y0 are the coordinates of the center of the circle.
If we expand the brackets in (1) and subtract R2 from the both sides, we'll get
x2−2xx0+x02+y2−2yy0+y02−R2=0.
Next we compare this formula and the given equation. We can see that −2xx0=−14x,−2yy0=−16y,
so x0=7,y0=8.
Therefore, x02+y02=113. From (1) and the given equation we get
x02+y02−R2=88.
Therefore, 113−R2=88,R2=25,R=5.
a) Center of the circle is (7, 8)
b) Radius is 5.
c) The area of the circle can be calculated as S=πR2=π⋅52=25π≈78.54.
d) Perimeter of the circle can be calculated as P=2πR=2π⋅5=10π≈31.42.
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