Find the equation of the circle which passes through the points P(1,0), Q(3,0) and R(0,2). Find also
(i) The coordinates of the other point in which the axis of y cuts the circle,
(ii) The coordinates of the other end of diameter through Q.

 

Dear student
We have,(1,0),(3,0),(0,2)Let the required circle be x2+y2+2gx+2fy+c=0     ...(1)It passes through (1,0),(3,0),(0,2)Substituting the coordinates of these points in eq(1):1+2g+c=0   ...(2)9+6g+c=0     ..(3)4+4f+c=0    ...(4)From eq(2), we havec=-1-2g   ...(5)Put this value in eq(3), we get9+6g-1-2g=08+4g=04g=-8g=-2 Putting the value of g in (5), we getc=-1-2-2c=3Putting the value of c in (4), we ge4+4f+3=0f=-74So, equation of the required circle=x2+y2-4x-72y+3=02x2+2y2-8x-7y+6=0
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