Question 1143791
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<pre>

The curve is a circle, and all you need is to find its radius.


For it, transform the given equation of a circle from its general form to its <U>standard form</U>.


For it, complete the squares for x- and y-terms separately in the given equation


    x^2 + y^2 - 3x - 8y + 18 = 0

    (x^2 - 3x) + (y^2 - 8y) = -18

    (x^2 - 3x + 2.25) + (y^2 - 8y + 16) = -18 + 2.25 + 16

    {{{(x-1.5)^2}}} + {{{(y-4)^2}}} = 0.25.


Thus you have the circle centered at the point (1.5,4) and having the radius of  r = {{{sqrt(0.25)}}} = 0.5.


The area of this circle is  {{{pi*r^2}}} = {{{pi*0.5^2}}} = {{{0.25*pi}}}.    <U>ANSWER</U>
</pre>

Solved.


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