A circle whose centre is the point of the intersection of the lines 2x-3y+4=0 and 3x+4y-5=0 passes through the origin. find its equation.
We are given equation of the lines-
----- (1)
----- (2)
By subtracting equation
from equation
,we get
By substituting in equation(1) we get,
Therefore, the center of the circle is
and equation of the circle will be
Since circle passes through the origin, so putting x = y = 0 in the above equation.
The equation of the circle becomes