the difference between the radii of largest and smallest circle which have their center on x2+y2+2x+4y-4=0 and pass through the point (a,b) lying outside given circle is.

Dear student

Draw the line passing through(a,b) and the center of the circle, meeting the circle at Pand Q. Pand Qare the nearest and the farthest points on the circle from (a,b). So they are the centers of the smallest and the largest circles. Ifddis the distance between (a,b)and the center of the given circle. Then the radii of the smallest and the largest circles are respectivelyd−3 and d+3. So their difference is6.

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