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## Find the equation of a circle which passes through the points `(4,1)` and `(6,5)` and having the centre on the line `4x+3y-24=0`. **Solution:** Let the equation of the circle be $x^2+y^2+2gx+2fy+c=0$. Let the centre be `C(+3,f)`. Given line is `4x+3y-24=0` `(4,1)`. `C(-9,f)` sub in above equat...

## Find the equation of a circle which passes through the points `(4,1)` and `(6,5)` and having the centre on the line `4x+3y-24=0`. **Solution:** Let the equation of the circle be $x^2+y^2+2gx+2fy+c=0$. Let the centre be `C(+3,f)`. Given line is `4x+3y-24=0` `(4,1)`. `C(-9,f)` sub in above equation `4(-9)+3(-f)-24=0` `-4g-3f-24=0` If `A(4,1)` sub in equation `(4)^2+(1)^2+2g(4)+2f(1)+c=0`. `16+1+8g+2f+c=0`. `8g+2f+c+17=0` If `B(6,5)` is sub in equation `(6)^2+(5)^2+2g(6)+2f(5)+c=0`. `36+25+12g+10f+c=0`