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If the normals at the points \mathrm{t_1} and \mathrm{t_2} intersect at the point −\mathrm{t_3} on the parabola\mathrm{y^2=4ax}, then \mathrm{t_1t_2}  is equal to  

 

Option: 1

1


Option: 2

2


Option: 3

\mathrm{t_3}


Option: 4

\mathrm{2t_3}


Answers (1)

best_answer

Normals at \mathrm{t_1 } and \mathrm{ t_2 } meets at some point \mathrm{\left(-t_3\right)}

\begin{aligned} & \mathrm{\Rightarrow -t_3=\left(-t_1-\frac{2}{t_1}\right)=\left(-t_2-\frac{2}{t_2}\right) }\\ &\Rightarrow \mathrm{ \begin{array}{c} \left(t_1-t_2\right)+2\left[\frac{1}{t_1}-\frac{1}{t_2}\right]=0 \quad \Rightarrow \quad \frac{\left(t_1 t_2-2\right)\left(t_1-t_2\right)}{t_1 t_2}=0 \end{array} }\\ & \mathrm{ \Rightarrow \quad t_1 t_2=2 }\\ \end{aligned}

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SANGALDEEP SINGH

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