Question

Please answer this question ​

Answer 1

$Let \: (x_{1}, y_{1}) = (at_{1}^{2} ,2at_{1}) \: and$

$(x_{2}, y_{2}) = (at_{2}^{2} ,2at_{2})$

$Slope \: of\:the \: line \: joining \: the \: given \: two$

$points = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$= \frac{2at_{2} - 2at_{1}}{ at_{2}^{2} - at_{1}^{2}}$

$= \frac{2\cancel {a}(t_{2} - t_{1})}{ \cancel {a}(t_{2}^{2} - t_{1}^{2})}$

$= \frac{2((t_{2} - t_{1})}{(t_{2}- t_{1})(t_{2} + t_{1})}$

$= \frac{2}{t_{1} + t_{2} }$

Therefore.,

$\red{Slope } \green { = \frac{2}{t_{1} + t_{2} } }$

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