Answer :

Given that the circle has the radius 10 and has diameters 2x + y = 6 and 3x + 2y = 4.



We know that the centre is the intersection point of the diameters.


On solving the diameters, we get the centre to be (8, - 10).


We have a circle with centre (8, - 10) and having radius 10.


We know that the equation of the circle with centre (p, q) and having radius ‘r’ is given by:


(x - p)2 + (y - q)2 = r2


Now we substitute the corresponding values in the equation:


(x - 8)2 + (y - ( - 10))2 = 102


(x - 8)2 + (y + 10)2 = 100


x2 - 16x + 64 + y2 + 20y + 100 = 100


x2 + y2 - 16x + 20y + 64 = 0.


The equation of the circle is x2 + y2 - 16x + 20y + 64 = 0.


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