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in Mathematics by (69.0k points)

Derive the equation of the circle passing through the point P(2, 8) and touches the lines 4x – 3y – 24 = 0 and 4x + 3y – 42 = 0 and coordinates of the centre less than or equal to 8.

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Here using Equations of bisectors of angle between the lines we will get co-ordinate of centre of circle i.e O. and as OA = OP we can obtain required equation of circle. consider O is the center of circle. 

and Let A and B denote the respective points of contact 

Equations of bisectors of angle between the lines are;  

Since O lies on one of these bisectors and x-coordinate of O is less then or equal to 8,

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