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Question

Find the equation of the circle passing through the point of intersection of the lines x + 3y = 0 and 2x - 7y = 0 and whose centre is the point of intersection of the lines x +y +1 = 0 and x - 2y + 4 = 0.

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Solution

The given equations of lines are
x+3y=0 (1)2x7y=0 (2)x+y1 (3)x2y=4 (1)
The general equation of circle with centre (a, b) and radius r is
(xa)2+(yb)2=r2 (A)
centre of (A) is the point of intersection of (iii) and (iv)
centre = (-2, 1)
(A)
(x+2)2+(y1)2=r2 (B)
Also, (A) passes through point of intersection of (1) and (2), that is through P = (0, 0)
22+(1)2=r2=r=5
Thus, the equation of required circle is
(x+2)2+(y1)2=5
or x2+y2+4x2y=0


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