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Centre of a circle which is orthogonal to the circle x^2+y^2=25 and (x-7)^2+(y-5)^2=4 and which has the least radius is

Centre of a circle which is orthogonal to the circle x^2+y^2=25 and (x-7)^2+(y-5)^2=4 and which has the least radius is

Grade:11

2 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
4 years ago
Condition of orhtogonality of 2 circles is

2 g g' + 2 f f' = c + c'

Apply this condition and keep in mind that radius of req circle should be least


Thanks
mycroft holmes
272 Points
4 years ago
Let the centres of the two circles be O1 and O2.
 
Any circle orthogonal to the two circles will have its centre on the radical axis and will pass through the limiting points of the co-axial system formed by the two given circles.
 
Its clear that among such circles, the one formed with the limiting points as the diameter will have the least radius. Hence we have to find the intersection of O1O2 and the radical axes. i.e. of the lines
 
5x = 7y and 14x+10y = 95 .

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