(a) Find the equation of the circle. (b) Find the area and circumference of the circle.
both a and b to complete solution
2026-04-22 15:06:38.1776870398
A circle is centered at (2, 1) and tangent to the line x+y=0.
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Given the centre of the circle lies at (2,1). So if the line x+y=0 is tangent to the given circle then the line joining point of contact of tangent to the circle and centre of the circle is perpendicular to the tangent as shown in figure
So the line parallel to tangent and passing through center is x+y=3
By using distance between two parallel lines we can find radius and radius is √2.
If we know the radius of the equation we can find all three questions given.
Equation of the circle is
$$(x-2)^2 +(y-1)^2 =2$$
Area is 2π
Circumference is2√2π