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**1.There is a circle with the equation x^2 + y^2 - 2ax = 0. A line is drawn through the centre of the circle which is parallel to the line x+2y=0. and also intersects the circle at A and B. Find the area of the triangle AOB.**

My attempt-

I calculated the slope of the given line(-1/2).So the equation of this line which cuts A and B on the circle would be y = -1/2x +c and as the line passes through the center of a circle which is drawn with origin as the center the equation turns y= -1/2x. The distance of A and B from the center is ax.So i would like to find the coordinates of A and B with that by-

ax = sqrt(x^2 + y^2) ---> which is true for both A and B. I'm stuck here.