If the points `(a ,0),(a t1 2,\ 2a t_1)a n d\ a t2 2,\ 2a t_2)` are collinear, write the value of `t_1t_2dot`

Explanation

For the points` (a, 0),(a t_{1}^{2}, 2 a_{1})` and` (a t_{2} 2,2 t_{2})` to be collinear, the following condition has to be met:


` [[a,0,1],[at_1^2,2at_1,1],[at_2^2,2at_2,1]]
`

`Rightarrow a(2 a t_{1}-2 a t_{2})-0+1(2 a^{2} t_{1}^{2} t_{2}-2 a^{2} t_{1} t_{2}^{2})=0 `

`Rightarrow 2 a^{2}(t_{1}-t_{2})+2 a^{2} t_{1} t_{2}(t_{1}-t_{2})=0`

`Rightarrow 2 a^{2}(t_{1}-t_{2})(1+t_{1} t_{2})=0 `

`Rightarrow(t_{1}-t_{2})=0 text { or }(1+t_{1} t_{2})=0 (a ne 0)`

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