Section formula for external division for JEE

Formula

\(P\left(\dfrac{mx_2-nx_1}{m-n},\dfrac{my_2-ny_1}{m-n}\right)\)

Variables: Point \(P\) divides \(A(x_1,y_1)\), \(B(x_2,y_2)\) externally in ratio \(m:n=AP:PB\).

Conditions: \(m\ne n\).

External division, harmonic division, conic and line problems.