Find the slope of a line passing through the following point:`(a t_1^2,2a t_1)a n d\ (a t_2^2,\ 2a t_2)`

Explanation

Slope `m=frac{y_{2}-y_{1}}{x_{2}-x_{1}}`

Given, `A(a at_{1}^{2}, 2 at_{1}), B(at _{2}^{2}, 2 at_{2})`


Therefore,

`m=frac{2 a t_{2}-2 a t_{1}}{a t_{2}^{2}-a t_{1}^{2}}=frac{2 a at(t_{2}-t_{1})}{a(t_{2}-t_{1})(t_{2}+t_{1})}`



`m=frac{2}{t_{1}+t_{2}}`