[Math] find the equation of the circle passing through the extremities of the diameter of the circle

analytic geometrycircles

find the equation of the circle passing through the extremities of the diameter of the circle

$x^2 +y^2 +2x-4y-2=0$

$x^2 +y^2 =0$

$x^2 +y^2 -6x-8y-2=0$

I cant understand what the question asks us to do.

Best Answer

I am not sure what is asked exactly in the question but if my guess is true it asks the equation of black circle enter image description here

Here $B$ denotes the center of the blue circle, $A$ denotes the center of the red circle and $H$ the center of the black circle. We know the coordinates of $B$ and $A$ hence we can find the equation of green line. After that if we solve the equation of the line with the red and the blue circles we can find coordinates of $E$ and $G$. We know the diameter of the big circle is the distance between $E$ and $G$ and the center of the big circle is mid point of $EG$. Therefore we can find the equation of the big circle.

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