write the equation of a circle with center at (a,b) and passing through the origin. geometry
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The circle we have to determine has its center at ( a, b) and passes through the origin. The radius of the circle is the distance between the points (0,0) and (a, b)
The radius is sqrt ( a^2 + b^2)
The equation of a circle with center ( a, b) and radius r is given by:
(x - a)^2 + ( y - b)^2 = r^2
Substituting the values we have:
(x - a)^2 + ( y - b)^2 = a^2 + b^2
=> x^2 + a^2 - 2ax + y^2 + b^2 - 2by = a^2 + b^2
=> x^2 + y^2 - 2ax - 2by = 0
The required equation of the circle is x^2 + y^2 - 2ax - 2by = 0
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